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IS" 



2: 




THE DETERMINATION 



OF 



HYDROGEN IONS 

An elementary treatise on the hydrogen electrode, indi- 
cator and supplementary methods with an indexed 
bibliography on applications 



BY 

W. MANSFIELD CLARK, M.A., Ph.D. 

Formerly Chemist, Research Laboratories of the Dairy Division, 

United Stales Department of Agriculture, 

Professor of Chemistry, Hygienic Laboratory, 

United States Public Health Service 



SECOND EDITION 



% l%o $ 



I O q 1<4. 



BALTIMORE 

WILLIAMS & WILKINS COMPANY 

1923 



QD 
50, \ 



First Edition, September, 1920 

Reprinted, May, 1921 

Second Edition, September, 1922 

Reprinted, May, 1928 



Copyright 1922 
Williams & Wilkins Company 

All rights reserved, including that of translation into foreign languages, 
including the Scandinavian 



To 

Fellow Workers in the Biological Sciences, 

Architects of Progress, 

Who Hew the Stone to Build Where Unseen Spires Shall Stand 



TABLE OF CONTENTS 

I. Introduction. Some General Relations Among Acids 

and Bases 15 

The nature of electrolytic dissociation 15 

Reversible reactions and chemical equilibria 16 

The equilibrium equation for acid dissociation 18 

The equilibrium equation for base dissociation 20 

The water equilibrium 21 

Titration curves 22 

Percentage dissociation curves 24 

Amphoters 30 

II. Some Special Aspects of Acid-base Equilibria 34 

" The pH scale 34 

/ The effect of dilution 37 

- Buffer action 39 

The conduct of strong electrolytes 44 

v/III. Outline of a Colorimetric Method 48 

Color chart. Water color by Broedel, color press work 

by F. Goeb between 50 and 51 

IV. Theory of Indicators 54 

Outline of the Ostwald theory 55 

Tautomerism 59 

Optical aspects 62 

V. Choice of Indicators 73 

Review of available material 74 

S0rensen's selection 78 

Clark and Lubs' selection 80 

Michaelis' selection 82 

Tables of indicators with their pH ranges 84-94 

Indicator synonyms 95 

VI. Standard Buffer Solutions for Colorimetric Comparison 99 
Preparation of materials for Clark and Lubs' solutions. 100 

Clark and Lubs' buffer solutions 106 

Preparation of materials for S0rensen's solutions 107 

S0rensen's solutions 111-114 

Other solutions 115 

VII. Sources of Error in Colorimetric Determinations 118 

Salt errors 118 

Protein errors 122 

Other errors 123 

Effect of temperature variation 123 

VIII. Approximate Determinations with Indicators 126 

Judgment by unaided eye 126 

Gillespie's method 127 

5 



6 CONTENTS 

Michaelis' method 132 

Indicator paper 138 

Dilution 139 

Use of indicators in bacteriology 140 

Special uses 142 

Spotting ' 143 

IX. Outline of the Electrometric Method 144 

X. Theory of the Hydrogen Electrode 151 

Potential differences between electrodes and solutions. . . . 151 
Derivation of equation relating electrode potential dif- 
ference to concentration 152 

Equation for concentration chain 154 

Derivation of numerical form of equation 155 

The "normal hydrogen electrode." 157 

Barometric correction 159 

Final working equation 161 

XI. Potential Differences at Liquid Junctions 163 

The cause 163 

Equations used in the calculation of liquid junction 

potential differences 164 

Experimental studies 167 

The employment of saturated KC1 solutions 168 

Summary of general conclusions 171 

XII. Hydrogen Electrodes and Electrode Vessels 173 

Construction of electrodes 173 

Deposition of "black." 175 

Hydrogen electrode vessels 178 

XIII. Calomel Electrodes 191 

The general principles and structure 191 

Chemical preparation of calomel 191 

Electro-chemical preparation of calomel 192 

Variations of potential 192 

Calomel electrode vessels 194 

Values assigned to potential differences 195 

XIV. The Potentiometer and Accessory Equipment 201 

The principle of the potentiometer 201 

A simple potentiometer 202 

The Leeds and Northrup instrument 203 

A resistance box system 205 

Volt-meter, system 207 

Ballistic galvanometer method of measurement 208 

Use of the electron tube 210 

Null point instruments 212 

The galvanometer 212 

The capillary electrometer 213 

The quadrant electrometer 214 

The telephone receiver 216 



CONTENTS 7 

Selection of null point instrument characteristics 216 

Potentiometer characteristics 219 

The Weston standard cell 221 

Storage batteries 224 

XV. Hydrogen Generators, Wiring, Shielding, Temperature 

Control, Purification of Mercury 227 

XVI. The Relation of Hydrogen Electrode Potentials to 

Reduction Potentials 242 

Relations based on assumption that reductant reacts with 

hydrogen ion or with water 243 

Difficulties encountered 245 

The postulate of electron concentration 247 

Electrode equation involving electron concentration 251 

Coordination of electrode equations 251 

Discussion based on the coordination 253 

Some elementary relations of hydrogen ion concentrations 

to observed "reduction potentials." 256 

XVII. Sources of Error in Electrometric Measurements of pH. 264 
XVIII. Standard Solutions for Checking Hydrogen Electrode 

Measurements 271 

XIX. The Standardization of pH Measurements 276 

Absence of a precise basis 277 ~ * 

Values used for standard electrodes 280 ct ft&tCfi 

Necessity for standardization 286 

Proposal of standard values 287 

i Experimental definition of pH 287*5 Ml Uit * 

XX. Supplementary Methods 289 cf fM f# 

The quinhydrone electrode 289 \'^/icc0uOUf 

Conductivity 293 fy /tfxsyfM 

Catalytic decomposition of nitrosotriacetonamine 294 (/ 

Catalytic decomposition of diazoacetic ester 295 

Inversion of cane sugar 296 

Catalyses in general 296 

Miscellaneous methods 296 

XXI. Applications 298 

General reviews 299 

The theory of titration 299 

General considerations 304 

Subject index to bibliography 310 

Bibliography 346 

Appendix 456 

Table A. Standard values for calomel electrodes 456 

Table B. Showing the relation of [H + ] to pH 456 

Table C. Temperature factors for concentration chains 457 

Table D. Correction of barometer reading for temperature 458 



8 i CONTENTS 

Table E. Barometric corrections for H-electrode potentials 459 

ce a 

Table F. Values of log and of log multiplied by the tem- 

1 — oc 1— a 

perature factors for concentration chains at 20°, 25°, 30° and 

37?5C 460-461 

Table G. Ionization constants 462-463 

Logarithms of numbers 464-465 

Index of authors mentioned in the text 467 

Index of Subjects 471 



PREFACE TO THE FIRST EDITION 

Poincare" in The Foundations of Science remarks, "There are 
facts common to several sciences, which seem the common source 
of streams diverging in all directions and which are comparable 
to that knoll of Saint Gothard whence spring waters which fer- 
tilize four different valleys." 

Such are the essential facts of electrolytic dissociation. 

Among the numerous developments of the theory announced 
by Arrhenius in 1887 none is of more general practical importance 
than the resolution of "acidity" into two components — the 
concentration of the hydrogen ions, and the quantity of acid 
capable of furnishing this ionized hydrogen. For two -reasons the 
hydrogen ion occupies a unique place in the estimation of stu- 
dents of ionization. First, it is a dissociation product of the great 
majority of compounds of biochemical importance. Second, it is 
the ion for which methods of determination have been best 
developed. Its importance and its mensurability have thus 
conspired to make it a center of interest. The consequent group- 
ing of phenomena about the activity of the hydrogen ion is 
unfortunate when it confers undue weight upon a subordinate 
aspect of a problem or when it tends to obscure possibilities of 
broader generalization. Nevertheless, such grouping is often con- 
venient, often of immediate value and frequently illuminating. 
Especially in the field of biochemistry it has coordinated a vast 
amount of material. It has placed us at a point of vantage from 
which we must look with admiration upon the intuition of men 
like Pasteur, who, without the aid of the precise conceptions 
which guide us, handled "acidity" with so few mistakes. 

In the charming descriptions of his experimental work Pasteur 
has given us glimpses of his discernment of some of the effects of 
"acidity" in biochemical processes. In the opening chapter of 
Studies on Fermentation he noted that the relatively high acidity 
of must favors a natural alcoholic fermentation in wine, while the 
low acidity of wort induces difficulties in the brewing of beer. 
He recognized the importance of acidity for the cultivation of 
the bacteria which he discovered and was quick to see the lack of 

9 



10 PREFACE TO FIRST EDITION 

such an appreciation in his opponents. In describing that process 
which has come to bear his name Pasteur remarks, "It is easy 
to show that these differences in temperature which are required 
to secure organic liquids from ultimate change depend exclusively 
upon the state of the liquids, their nature and above all upon the 
conditions which affect their neutrality whether towards acids or 
bases." The italics, which are ours, emphasize language which 
indicates that Pasteur was aware of difficulties which were not 
removed till recently. Had Pasteur, and doubtless others of like 
discernment, relied exclusively upon volumetric determination of 
acidity they would certainly have fallen into the pitfalls which 
at a later date injured the faith of the bacteriologist in the meth- 
ods of the chemist. Was it reliance upon litmus which aided 
him? Perhaps the time factor involved in the use of litmus 
paper, which is now held as a grave objection, enabled Pasteur 
to judge between extremes of reaction which the range of litmus 
as an indicator in equilibrium does not cover. At all events he 
recognized distinctions which we now attribute to hydrogen ion 
concentrations. Over half a century later we find some of 
Pasteur's suggestions correlated with a marvelous development 
in biochemistry. The strongest stimulus to this development 
can doubtless be traced to the work of S0rensen at the Carlsberg 
Laboratory in Copenhagen and not so much to his admirable 
exposition of the effect of the hydrogen ion upon the activity of 
enzymes as to his development of methods. At about the same 
time Henderson of Harvard, by setting forth clearly the equilibria 
among the acids and bases of the blood, indicated what could be 
done in the realm of physiology and stimulated those researches 
which have become one of the most beautiful chapters in this 
science. 

Today we find new indicators or improved hydrogen electrode 
methods in the physiological laboratory, in the media room of 
the bacteriologist, serving the analyst in niceties of separation 
and the manufacturer in the control of processes. The material 
which was admirably summarized by Michaelis in 1914, and to 
which Michaelis himself had contributed very extensively, pre- 
sents a picture whose significance he who runs may read. There 
is a vast field of usefulness for methods of determining the hydro- 
gen ion. There is real significance in the fruits so far won. 



PREFACE TO FIRST EDITION 11 

There remain many territories to explore and to cultivate. We 
are only at the frontier. 

In the meantime it will not be forgotten that our knowledge of 
the hydrogen ion is an integral part of a conception which has 
been under academic study for many years and that the time has 
come when the limitations as well as certain defects are plainly 
apparent. While there is now no tendency nor any good ground 
to discredit the theory of electrolytic dissociation in its essential 
aspects, there is dissatisfaction over some of the quantitative 
relationships and a demand for broader conceptions. It requires 
no divination to perceive that while we remain without a clear 
conception of why an electrolyte should in the first instance 
dissociate, we have not reached a generalization which can cover 
all the points now in doubt. Perhaps the new developments in 
physics will furnish the key. When and how the door will open 
cannot be foreseen ; but it is well to be aware of the imminence of 
new developments that we may keep our data as pure as is con- 
venient and emphasize the experimental material of permanent 
value. We may look forward to continued accumulation of 
important data under the guidance of present conceptions, to 
distinguished services which these conceptions can render to 
various sciences and to the critical examination of the material 
gathered under the present regime for the elements of permanent 
value. These elements will be found in the data of direct experi- 
mentation, in those incontrovertible measurements which, though 
they be but approximations, have immediate pragmatic value 
and promise to furnish the bone and sinew of future theory. In 
the gathering of such data guiding hypotheses and coordinating 
theories are necessary but experimental methods are vital. 

The time seems to have come when little of importance is to 
be accomplished by assembling under one title the details of 
the manifold applications of hydrogen electrode and indicator 
methods. It would be pleasing to have in English a work com- 
parable in scope with Michaelis' Die W asserstoffionenkonzentra- 
tion; but even in the short years since the publication of this 
monograph the developments in special subjects have reached 
such detail that they must be redispersed among the several sci- 
ences, and made an integral part of these rather than an unco- 
ordinated treatise by themselves. There remains the need, for a 



12 PREFACE TO FIRST EDITION 

detailed exposition, under one cover, of the two methods which 
are in use daily by workers in several distinct branches of bio- 
logical science. It is not because the author feels especially 
qualified to make such an exposition that this book is written, 
but rather because, after waiting in vain for such a book to 
appear, he has responded sympathetically to appeals, knowing 
full well from his own experience how widely scattered is the 
information under daily requisition by scores of fellow workers. 

For the benefit of those to whom the subject may be new 
there is given in the last chapter a running summary of some of 
the principal applications of the methods. This is written in 
the form of an index to the bibliography, a bibliography which 
is admittedly incomplete for several topics and unbalanced in 
others, but which, it is believed, contains numerous nuclei for 
the assembling of literature on various topics. 

The author welcomes this opportunity to express his apprecia- 
tion of the broad policy of research established in the Dairy Divi- 
sion Laboratories of the Department of Agriculture under the 
immediate administration of Mr. Rawl and Mr. Rogers. Their 
kindness and encouragement have made possible studies which 
extend beyond the range of the specialized problems to which 
research might have been confined and it is hoped that the bread 
upon the waters may return. To Dr. H. A. Lubs is due the credit 
for studies on the synthesis of sulfonphthalein indicators which 
made possible their immediate application in bacteriological 
researches which have emanated from this laboratory. Acknowl- 
edgment is hereby made of the free use of quotations taken 
from the paper The Colorimetric Determination of Hydrogen Ion 
Concentration and Its Applications in Bacteriology published in 
the Journal of Bacteriology under the joint authorship of Clark 
and Lubs. 

The author thanks his wife, his mother, Dr. H. W. Fowle and 
Dr. H. Connet for aid in the correction of manuscript and proof, 
and Dr. Paul Klopsteg for valuable suggestions. 

It is a pleasure to know that the publication of the photograph 
of Professor S. P. L. S0rensen of the Carlsberg Laboratory in 
Copenhagen will be welcomed by American biochemists all of 
whom admire his work. 

Chevy Chase, Maryland 
March 17, 1920 



PREFACE TO THE SECOND EDITION 

The first edition of this book was offered to fellow workers for 
the reasons stated in the preface. The rapid exhaustion of two 
printings has revealed the extent of the demand for information 
upon the topics discussed; but it has also brought to the author a 
disquieting realization of the responsibility assumed at the first 
venture, and regret that his preoccupation in a distinctive 
although allied realm of research has prevented investigations which 
might have contributed data for a more complete second edition. 
This same preoccupation may be offered as an excuse for the 
deficiencies in the bibliography and its classification. Over 900 
new references have been added to the eleven hundred odd said 
to be in the first edition; but, when it is realized that much of the 
newer information is contained in papers neither the title nor 
general subject of which would indicate that hydrogen ion con- 
centrations have been considered, it will be appreciated that the 
task of the bibliographer requires more time than an investigator 
can afford. Indeed it will not be long before it will be as difficult 
to trace this information as it has become to trace all the effects 
of temperature. In certain fields of investigation "pH" is becom- 
ing almost as common as "°C." Were it not that the introduction 
of a new symbol would introduce confusion we would wish that 
the special interpretation of pH given in Chapter XVII of the 
first edition (Chapter XIX, this edition) could be symbolized by 
°S (degrees S0rensen). 

Certain chapters of the first edition have been rewritten and 
all have been expanded to bring the book up to date and to meet 
the very helpful suggestions given in the generous reviews of the 
first edition, or by personal correspondence. It has been advis- 
able, however, either to balance one suggestion against another 
or to rely upon one's own judgment to maintain a balance in the 
general treatment. 

The question of a change of treatment to conform throughout 
to the "activity" concept has been given serious consideration. 
The author has been counseled by experienced teachers not to 
attempt such a change, but his chief reason for definitely rejecting 

13 



14 PREFACE TO SECOND EDITION 

the -proposal is simply that most of the data in use are still in 
terms of the older conceptions. In the recasting of this data a 
great deal of new experimental material must be collected and 
the newer conceptions must be stabilized. Anything short of a 
thorough revision of existing data would be but to cover the 
subject with a thin veneer giving the appearance rather than 
the substance of an up-to-date treatment. 

The author is indebted to so many people for helpful sugges- 
tions that it would appear ungracious to mention but a few. How- 
ever, due credit must be given to Dr. Barnett Cohen for pains- 
taking correction of proof, to Miss Florence Lansdale for clerical 
assistance and to the publishers for their unfailing and courteous 
cooperation. 

Chevy Chase, Maryland 
May 22, 1922 



CHAPTER I 

Introduction — Some General Relations Among Acids 

and Bases 

In a country rich in gold observant wayfarers may find nuggets on 
their path, but only systematic mining can provide the currency 
of nations. — F. Gowland Hopkins. 

Why certain solvents such as water should cause or permit 
the splitting of a compound into electrically charged bodies, 
called ions, has not yet been very clearly explained. That they 
do has been demonstrated with reasonable certainty. The evi- 
dences are described in texts of physical chemistry and will not 
be reviewed here, except as they are revealed in the verification 
of the laws of chemical equilibria among electrolytes. 

That aspect of electrolytic dissociation which is of special 
interest to us may be conveniently pictured as follows. 

A chemical element is conceived to be an aggregate of unit, 
negative, electrical charges (electrons) grouped at relatively 
enormous distances about a central, neutralizing nucleus of 
positive electricity. The numerical value of this nucleus, in 
terms of the number of electrons required for neutralization, and 
the geometrical configuration of the positions of the surrounding 
electrons are supposed to distinguish the several elements. 

Certain of the electrons are but weakly incorporated in the 
planet-like system of certain elements. When such an electron 
has escaped, the element is left with a unit excess of positive 
electricity. It is then a positive ion, a cation, having distinctive 
properties. 

If an element is so constituted that it can hold an extra electron, 
the extra charge gives it new characteristics. The negatively 
charged element is called an anion. 

Certain compounds such as HC1 are made up of elements of 
the two types mentioned above. On electrolytic dissociation HC1 
oreaks up in such a way that the hydrogen atom loses an electron 
ind this is taken up by the chlorine atom. HC1, thus, dissociates 

15 






16 THE DETERMINATION OF HYDROGEN IONS 

into the positively charged hydrogen ion and the negatively 
charged chlorine ion. The process may be represented as follows: 

HC1?±H+ + Cl- 
in the case of complex compounds such as acetic acid a similar 
exchange of an electron occurs. The group CH 3 COO acts as a 
unit and when negatively charged becomes the acetate anion. 

Frequently an element or group can lose or acquire several elec- 
trons. For instance Ca ++ is the divalent cation of calcium and 
SO4 is the divalent anion of the sulfate group — called divalent 
because there are concerned two of those electrons which are sup- 
posed to be intimately connected with the phenomenon of valency. 

In passing it is interesting to note that the hydrogen ion is 
unique. The element hydrogen is supposed to have but one 
electron to the atom. When this is lost there is left the hydrogen 
ion, a lone unit, positive charge. 

Now this pictorial conception of the structure of elements, 
while pregnant with possibilities, must not be considered vital 
to the subject at hand. The one aspect which is vital is that 
there occur dissociations whereby an element or group becomes 
electrically charged — positively or negatively, as the case may be. 
It is the electrical charge which turns an element or group into a 
virtually new body and at the same time furnishes a handle, as 
it were, with which we may lay hold on it by electrical devices. 

On the other hand the electrical charge does not prevent a 
limited application to ions of the laws of chemical equilibria. 
Indeed it is among dilute solutions of certain electrolytically 
dissociated compounds that there have been found the most 
exact data supporting the laws of chemical equilibria. 

It is with these laws of chemical equilibria that we are chiefly 
concerned when dealing with the measurement of and the effects 
of hydrogen ion concentration. Therefore, if electrolytic ioni- 
zation be granted as a fact, it is only necessary to sketch the 
concept of chemical equilibrium before coming to the simple, if 
somewhat detailed account of the special manner in which the 
concept is applied to acid-base equilibria. 

Consider an acid of the type HA dissociating into tue cation 
H+ (hydrogen ion) and the anion A - . The process may be 
expressed as follows: 

HA ^± H+ + A" (1) 



GENERAL RELATIONS AMONG ACIDS AND BASES 17 

Arrows are used to indicate that the process is reversible, — 
that among the large number of anions and cations present in a 
given volume some are recombining to form HA the while a 
portion of the HA molecules are dissociating. 

This concept of a "reaction" as labile, continuous, reversible 
is of profound importance. So long as analysts are content to 
balance the two sides of a written reaction with regard only to 
the stoichiometrical relations, it is convenient to use the equation 
sign and to forget the reality implied in the use of arrows. Reac- 
tions do not go to completion and only approach completion 
when by design or chance the proper conditions are supplied. 
This reversibility of chemical reactions displays a world in flux. 
From it the "everlasting hills" cannot escape; but upon it life bal- 
ances its intricate organization. Often this is done so nicely that 
the life of certain organisms is almost immortal. 

In this interminable interplay of chemical reactions there occur 
situations when on the statistical average a given reaction is pro- 
ceeding no faster in one direction than in the other. In such 
circumstances a chemical equilibrium is said to occur. Let us 
formulate in as simple a way as possible the condition of a chemical 
equilibrium. 

Let brackets placed about a symbol indicate concentration of 
the bracketed "species." Thus [HA] represents the concentration 
of the residual, undissociated acid HA. Throughout the following 
discussions we shall always let it be implied that by "concentra- 
tion" is meant molar concentration. A molar solution is one 
containing in one litre of solution that number of grams of the 
indicated substance which is equal to its formula weight. 

In equation (1) the rate at which the concentration [HA] is 
being diminished because of the ionization may depend upon 
several physical conditions. To know these is unnecessary for 
the purpose at hand if we may assume that their effect on the 
individual molecules of HA is constant on the statistical average. 
Then, obviously, the rate at which reaction (1) proceeds from 
left to right will depend upon the concentration of HA and some 
constant factor which will be called ki. 

Velocity left to right = ki [HA] (2) 

The velocity of the reverse reaction wherein the ions recombine 
to form HA might be supposed to be dependent only upon the 



18 THE DETERMINATION OP HYDROGEN IONS 

rate at which the ions in their thermal agitation collide. But it 
is difficult to say what degree of approach is necessary for com- 
bination or what other conditions must be fulfilled before the 
combination can be considered to have taken place. It is much 
safer then to assume only that some degree of meeting is necessary, 
that some average state is to be considered virtual combination 
and that the physical factors bringing about this state are, on 
the statistical average, constant. Here again then we ascribe 
the velocity of the reaction first to a factor dependent solely 
upon the numbers of ions concerned [concentration] and second 
another factor embracing all the known and unknown influences, 
exclusive of concentration. Suppose then that we start with 
equal numbers of H + ions and A~ ions and double the concen- 
tration of H + . Evidently the number of collisions of H + ions 
with A - ions will double. Likewise, if [A - ] is doubled, the number 
of collisions of A - with H + ions will be doubled. If both are 
doubled, the collisions are quadrupled. Consequently the velocity 
of association, in so far as it is dependent upon the concentrations 
of the reactants, is proportional to the product of these concen- 
trations. Introducing the unknown proportionality factor repre- 
senting the constant effect of all physical influences, we have : 

Velocity right to left = k 2 [H+] [A-]. (3) 

We have already said that the state of equilibrium occurs when 
the velocity of the reaction in one direction equals the velocity in 
the reverse direction. Then at once by combining (2) and (3) 
we have: 

[H + ] [Aj _ kx , 

[HA] ~ k 2 ~ Ka W 

For the ratio of two constants there is substituted in (4) another 
constant, K a , known as the equilibrium constant. This equilib- 
rium constant when applied to electrolytes is known as the 
ionization or dissociation constant. 1 

1 It should be particularly noted that in equation (4) the brackets 
symbolize the concentrations occurring at the equilibrium state. When- 
ever numerical values are to be introduced it is to be assumed that there 
will be employed the same unit of concentration that was used in the experi- 
mental derivation of K a , and also the conventional form of the ratio with 
the ions in the numerator. 



GENERAL RELATIONS AMONG ACIDS AND BASES 19 

Since equation (4) deals with the active masses of the reactants 
it is a special application of the so-called law of mass action which 
states that the velocity of a reaction is proportional to the product 
of the concentrations of the reactants. 

Using equation (4) for a particular acid it will be seen by inspec- 
tion of the equation that if [H + ] is increased, as by the addition 
of another acid, there must be a readjustment of either [A - ] or 
[HA] or both to keep K a constant. Likewise if [A~] should be 
increased by the addition of a highly dissociating salt of the acid in 
question, there would be a readjustment of either [H + ] or [HA] or 
both to keep K a constant. Thus the independent alteration of 
the concentration of any one of the species included in the equi- 
librium equation causes a displacement of the equilibrium to a 
new position. This illustrates how difficult it is to keep track of 
the affair unless use is made of the simple algebraic relations. 

If the acid alone be present, [H+] = [A - ]. Substituting [H + ] 
for [A - ] and solving equation (4) for [H+] we have 



[H+] = VK a [HA] 

If the acid is so weak that practically all is in the undissociated 
form, no great error is made in putting [HA] equal to the con- 
centration [S] of the total acid. Then [H+] = VKJS]". 

In general it can be shown that for any reaction such as 

A + B + C + . . . . . ;=± A' + B' + C + 

the equilibrium condition is: 

[A] [B] [C] . . . 



[A'] IB'] [CI 



= k 



From the assumptions introduced in the argument it is evident 
that the equilibrium constant will hold good only so long as there 
are maintained constant those physical conditions which affect 
the velocity of a reaction in one direction or the reverse. A 
change in temperature will alter the "constant," but not to such 
an extent as will a change in solvent. With due regard for such 
matters we may regard the equilibrium constant as a number 
characteristic of a given reaction at the equilibrium state. 

In the derivation of the equilibrium equation we have employed 
as an example the electrolytic dissociation of an acid. We may 



20 



THE DETERMINATION OF HYDROGEN IONS 



now state that all substances capable of yielding hydrogen ions 
must be considered as having an acidic nature and their conduct 
in solution must be governed by the equilibrium equation. 

With the ionization constant denned we are prepared to give 
quantitative significance to comparative "strengths" among acids. 
Inspection of equation (4) shows at once that if K a is large the 
numerator of the left hand side must be large in relation to the 
denominator. In other words an acid having a relatively high 
K a value will, if left to itself in solution, tend toward a high degree 
of dissociation. A given over-all concentration of an acid with 
high dissociation constant will furnish a higher concentration of 
hydrogen ions than will the same over-all concentration of an 
acid with low dissociation constant. Thus the value of K a at 
once indicates the "strength" of an acid so far as "strength" is 
measurable in terms of ionization. 

In the following table are given a few dissociation constants 
of acids and also of bases. 

TABLE 1 

Showing acidic and basic dissociation constants and their relation to a rough 

classification of acids and bases 



CLASS 


COMPOUND 


DISSOCIATION CONSTANT 


Strong acid 


Hydrochloric 
Oxalic (first H) 
Acetic 
Boric 

Sodium hydroxid 
Ammonium hydroxid 
Aniline 


Not well defined 


Weak acid 


1.1 X 10" 1 
1.8 X 10 _s 


Very weak acid 


6.5 X 10 _1 ° 


Strong base 


Not well defined 


Weak base 


1.8 X 10 -s 


Very weak base 


4.6 X 10~ 10 







The dissociation of bases will now be considered. Just as a 
substance ionizing to give hydrogen ions is called an acid so a 
substance which ionizes to give hydroxyl ions (OH - ) is called 
a base. 

The reversible reaction NaOH ^ Na+ + OH~ may be written 
as BOH ^± B + + OH - where B represents any monovalent 
metal. This reaction may be treated in precisely the same way 
that reaction (1) was treated. The equilibrium condition is: — 



[B+] [QH- 
[BOH] 



= K b 



(5) 



GENERAL RELATIONS AMONG ACIDS AND BASES 21 

Just as the value of K a is characteristic of a given acid so is 
the value of Kb characteristic of a given base. 

A very important relationship between acids and bases in 
aqueous solution is brought about by the conduct of water. 
It dissociates into the hydrogen ion (H + ) characteristic of acids 
and the ion characteristic of bases, OH - , called the hydroxyl ion. 
The equilibrium of the reversible reaction HOH ^± H + + OH - is 
represented by 

[H+] [OH-] _ 
[HOH] 

Because the concentration of the undissociated water is so 
large in relation to the dissociation products, [HOH] will not be 
changed appreciably by the slight dissociation. [HOH] may 
therefore be considered a constant and combined with k. Then 
the above equation becomes: 

[H+] [OH-] - K w . (6) 

It follows from this equation that, no matter how concentrated 
the hydroxyl ions may be, there must remain sufficient hydrogen 
ions to satisfy the above relation. 2 This permits us to speak of 
the hydrogen ion concentration of alkaline solutions and, as will 
be shown presently, to construct a scale of acidity-alkalinity in 
which we do not discriminate between hydrogen and hydroxyl 
ion concentration. 

Starting from equations (4), (5) and (6), applying certain 
approximations and then using graphic methods of presentation 
we can present a generalized picture of the conduct of acids and 
bases similar to that first used by Henderson (1908). The final 
simplicity of the picture warrants what may at first appear to be 
a complicated reconstruction of the above equations. 

In order to emphasize the hydrogen ion concentration as the 
quantity in equation (4) with which the other species keep in 
adjustment, let us rewrite equation (4) as follows: 

1 [A-] 



[H+] K a [HA] 

* K w = 10 -14 . If in an alkaline solution the concentration of hydroxyl 

*. Kw in -14 

ions is 0.01 normal (10~ 2 ), [H+] = : — ^-r = =— = 10" 12 N. 

[OH"] 10~ 2 



22 



THE DETERMINATION OF HYDROGEN IONS 



We choose the form which will give the reciprocal of [H + ] 
because we shall have to make use of the logarithm of this value 
under the symbol pH for reasons which will appear later. For 
the present let it be granted that it will be found convenient to 

use log rather than [H + ]. Taking the logarithm of each 

[H+J 

side of the above equation we have 



i i . i, . [Ai 

log • = log 1- log ; 

[H + ] K a * [HA] 



(7) 



P H 



























%J 


s. 








































* 


I A 


■ 


( 


> i 


* 10 



cc 

Fig. 1. Comparison of Experimental' Titration Curve of Acetic Acid 
with Theoretical Approximation 

With the use of this equation we can chart some important 
relationships. Let it first be applied to what may be called 
"titration curves." 

Suppose we titrate 10 cc. of 0.2n acetic acid with 0.2n sodium 
hydroxid. Ordinarily no attention would be given to the state 
of the solution until the so called "end point" of the titration 
were reached. In the present instance we shall follow the course 
of the titration from the beginning by determining after each 
addition of alkali the hydrogen ion concentration. 



GENERAL RELATIONS AMONG ACIDS AND BASES 



23 



The experimental curve is plotted in figure 1. Let us com- 
pare it with the values obtained by the use of equation (7) . 

In the first place acetic acid is classed among the moderately 
weak acids. Its dissociation constant as given in Landolt- 

Bornstein is 1.82 X 10" 5 at 18°C. Hence log =r = 4.74. Be- 

-t»-a 

TABLE 2 

Comparison of log 1/[H + ] for acetic acid-sodium acetate calculated by means of 

the approximation formulated in equation (8) and determined 

experimentally by Walpole 



N/5 NaOH 


RATIO 

[salt] 
[acid] 


LOG RATIO 


log 1/Ka 


LOG 1/[H+] 
CALCULATED 


LOG 1/[H+] 
WALPOLE 


cc. 

0.20 


9.00 


-1.69 


4.74 


3.05 


3.08 


0.25 


0.020 


-1.59 


4.74 


3.15 


3.15 


0.30 


0.026 


-1.51 


4.74 


3.23 


3.20 


0.40 . 


0.031 


-1.38 


4.74 


3.36 


3.32 


0.50 


0.042 


-1.28 


4.74 


3.46 


3.42 


0.75 


0.053 


-1.09 


4.74 


3.65 


3.59 . 


1.0 


0.081 


-0.95 


4.74 


3.79 


3.72 


2.0 


0.111 


-0.60 m 


4.74 


4.14 


4.05 


3.0 


0.250 


-0.37 


4.74 


4.37 


4.27 


4.0 


0.429 


-0.18 


4.74 


4.56 


4.45 


5.0 


0.667 


0.00 


4.74 


4.74 


4.63 


6.0 


1.000 


+0.18 


4.74 


4.92 


4.80 


7.0 


1.500 


+0.37 


4.74 


5.11 


4.99 


7.5 


2.33 


+0.48 


4.74 


5.22 


5.09 


8.0 


3.00 


+0.60 


4.74 


5.34 


5.23 


8.5 


4.00 


+0.75 


4.74 


5.49 


5.37 


9.0 


5.67 


+0.95 


4.74 


5.69 


5.57 


9.5 


19.00 


+1.28 


4.74 


6.02 


5.89 


9.625 


25.67 


+1.41 


4.74 


6.15 


6.02 


9.75 


39.00 


+1.59 


4.74 


6.33 


6.21 


9.875 


79.00 


+1.90 


4.74 


6.64 


6.52 



cause of the small dissociation of acetic acid (less than 2 per cent 
in 0.2n solution even with no acetate present) the concentration 
of the undissociated residue [HAc] is approximately equal to the 
concentration of the total acetic acid. It is characteristic of the 
alkali salts of acids that they are very highly dissociated. There- 
fore, when sodium hydroxid is added to the acetic acid solution, 
the resulting sodium acetate furnishes the greater amount of the 






24 THE DETERMINATION OF HYDROGEN IONS 

total acetate (Ac~) ions. As an approximation therefore we 

[A-] [salt] 

may substitute for the ratio 7777", in equation (7) the ratio 7 — — • 

[HA] [acid] 

Equation (7) then becomes: 

log J_ =log-L + log^-j. (8) 

*[H+J & K a *[acid] 

[ salt] 
In table 2 are given the ratios r — 77. calculated from the num- 

[acid] 

ber of cubic centimeters of 0.2n alkali added to 10 cc. of 0.2n 

acetic acid. Then follow the logarithms of these ratios, the value 

of log z?~ for acetic acid, and log 7777; calculated from these data 

-TV a L-H- J 

by means of equation (8). Finally in the last column are given 

the values of log ,777; calculated by Walpole (1914) from his 

l**TJ 
hydrogen electrode measurements. The experimental values 

pH = log 7777; are plotted in figure 1 as circles while the values 
LJfcr«-j 

calculated by means of the approximation equation (8) are on the 

unmarked line. There is evidently a substantial agreement with 

a more or less regular discrepancy which remains to be explained. 

The discrepancy may be ascribed in part to the assumption that 

the salt is wholly dissociated and that it is entirely responsible 

for the anions of equation (7). If there be applied a correction 

for the partial dissociation of the acetate, there is obtained a 

much closer agreement. 

But even this correction does not take into consideration cer- 
tain minor points, and it leaves untouched both the accuracy with 
which K a has been determined and the comparability of data 
obtained by widely different methods which are often applied 
(sometimes uncritically) in making such calculations as those 
indicated above. 

We shall proceed with the approximate treatment to bring out 
certain more general relations, and shall leave to Chapter XXI 
their further application to ordinary titrations. 

[salt] 1 

In equation (8) when the ratio f — rrr equals one, log J777; = 

log 77 Then [H+] = K.. 



GENERAL RELATIONS AMONG ACIDS AND BASES 25 

In other words the middle portion of the titration curve of a 
particular acid lies at ("near" if we are # to be strict) a point 
where the hydrogen ion concentration is numerically equal to the 
dissociation constant. 3 

Thus if one wishes a solution of [H + ] = 1 X 10~ 5 , an acid with 
dissociation constant close to this value is selected and mixed 
with the proper amount of its alkali salt. 

Or to look at the matter from another point of view, if we 
determine the half transformation point in the titration of a 
weak acid, we know approximately the dissociation constant of 
the acid. 

A similar set of relationships can be constructed for bases. 

Instead of putting the fundamental equation (4) into the 
form which we have utilized in following titration curves it is 
sometimes advantageous to use the following development. 

Transforming (4) we have : 

[A-] _ K a 
[HA] [H+] 

Now let us represent the concentration of the total acid by [S]. 
Then the concentration of [HA] will be : 

[HA] = [S] - [A-] 

[A~] K a 

[S]-[Ai [H+] 
or 

[A-] K a 



[S] K a + [H+] 

[A-] 
The ratio -rrr- is the ratio of the dissociated acid to the total acid 
L»J 

present in the solution. This ratio may be represented by a. 
Hence, 

K a 



K a + [H+] 



(9) 



3 There is implied in this the maintenance of the customary unit of 
concentration. Cf. page 18. 



26 THE DETERMINATION OF HYDROGEN IONS 



/ 1 \ /^ — \ 

Since we are interested in log rrrp: or pH rather than [H+], because 

of the resultant simplification of chart representations and because 
of other reasons which will appear later, we may recast equation 
(9) and taking the logarithm of each side we have : 

11 ot 

log = log h log — (10) 

* [H+] * K. * (1 - «) 

Plotting log } which is pH, against «, and expressing « as 

[H + J 

percentage dissociation, there is obtained a curve such as A or B 
in figure 2. Such curves are identical in form, the form being 

Ot * 

determined by the ratio — • Their position on the pH axis 

(1 - «) 
is determined by the value of the dissociation constant in the 

expression log — 

Since (10) is useful in plotting type curves a table of values for 

log is given in the appendix (p. 460). 

1 — a 



(11) 



In a similar way we arrive at the relation for bases : 

a= Kb 

" K b + [OH-] 
or 

logfOHi^log 1 ^ 1 " 00 - (12) 

a 

But since we wish to deal uniformly with log jTT^f, which is pH, 

rather than with the hydroxyl ion concentration or any direct 
function thereof, we shall introduce the water equilibrium, equa- 
tion (6). Then (12) becomes 

log JEz. = log ?EiiL^ 

[H+] « 

or 

pH = log-L = log |^ + log 9—-^ (13) 

[H+] K w ot 



GENERAL RELATIONS AMONG ACIDS AND BASES 



27 



With the introduction of K w , the dissociation constant of water, 
into our equations it becomes advisable to consider its numerical 
value. K w has been determined in a variety of ways of which 
the following are examples. Kohlrausch and Heydweiller (1894) 
determined the electrical conductivity of extremely pure water. 
Assuming that the conductance is proportional to the mobility of 




Fig. 2. Dissociation Cueves and Dissociation-Residue Curves 

A. Dissociation curve of acid, log — = 8.0. 

K a 

B. Dissociation curve of acid, log — = 4.8. 

C. Dissociation-residue curve of acid, log — = 4.8, or dissociation curve 

K a 

of a base log — = log — - — 4.8. 
Kb K w 

the hydrogen and the hydroxyl ions, and that these are present in 
equal concentrations, their product is found to be 1.1 X 10~ 14 . 
The hydrolysis of methyl acetate having been found to be pro- 
portional to the concentration of hydroxyl ions, Wijs (1893) 
determined the hydrolysis by water and found K w = 1.44 

X io- 14 . 

By determining the hydrogen ion concentration with the 
hydrogen electrode in solutions of known hydroxyl ion con- 
centration (as determined by conductance measurements), K w 
is obtained from the product of the concentrations of the two ions. 



28 



THE DETERMINATION OF HYDROGEN IONS 



By this method Lewis, Brighton and Sebastian (1917) found 
the value 1.012 X 10" 14 at 25°C. 

Kolthoff (1921) has compiled the following table showing the 
dissociation constant of water at different temperatures as given 
by different authors and methods: 



TEMPER- 
ATURE 


i 


ii 


in 


IV 


0° 


0.12 X 10" 14 


0.14 X 10~" 




0.089 X 10-" 


18° 


0.59 X 10~ 14 


0.72 X 10"" 


0.74 X 10~" 


0.46 X 10"" 


25° 


1.04 X 10"" 


1.22 X 10"" 


1.27 X 10"" 


0.82 X 10-" 


50° 


5.66 X 10~" 


8.7 X 10"" 






100° 


58.2 X 10~ 14 


74.0 X 10~ 14 




48.0 X 10-" 



I. Kohlrausch and Heydweiller recalculated by Heydweiller (1909). 

II. Lorenz and Bohi (1909). 

III. Michaelis (1914). 

IV. Noyes and coworkers (1907). 



The following values of log zz~ given by Michaelis (1914) were 

X\-W 

obtained on a somewhat different basis from that used by Lewis, 
Brighton and Sebastian (1917). 

Since in pure water [H+] = [OH"], [H+] or [OH~] = VK W . 
Hence from the datum of Lewis, Brighton and Sebastian the 
normality of H + or OH - in pure water at 25°C. is VK W = 1.006 
X 10~ 7 (practically pH = 7.0). 

In the following pages wherever we have occasion for purposes 
of illustration to use a numerical value for K w we shall employ the 
rounded value 10 -14 . 

Introducing the numerical value of K w into equation (13) 
we have the convenient form : 



1 , (1 — «) 
pH = 14 - log -=- + log i 1 

K b a 



(14) 



In figure 2 we have plotted a as percentage dissociation. It is 
obvious that the percentage dissociation residue will give the 
complement of the dissociation curve and will cross any partic- 
ular one of these at the fifty per cent dissociation point. See, for 
example, the curve C of figure 2. 



GENERAL RELATIONS AMONG ACIDS AND BASES 



29 



Now by comparing equation (10) with equation (14) it is found 
that the curve for the dissociation-residue of an acid is identical 
with the curve for the dissociation of a base when K a of the acid 

is related to K b of the base as log ^r = 14 — log — . In other 



K, 



TABLE 3 



Kb 



TEMPERATURE 


l 

LOGTf— 
K W 


pH OP NEUTRAL POINT 


16 


14.200 


7.10 


17 


14.165 


7.08 


18 


14.130 


7.07 


19 


14.100 


7.05 


20 


14.065 


7.03 


21 


14.030 


7.02 


22 


13.995 


7.00 


23 


13.960 


6.98 


24 


13.925 


6.96 


25 


13.895 


6.95 


26 


13.860 


6.93 


27 


13.825 


6.91 


28 


13.790 


6.90 


29 


13.755 


6.88 


30 


13.725 


6.86 


31 


13.690 


6.85 


32 


13.660 


6.83 


33 


13.630 


6.82 


34 


13.600 


6.80 


35 


13.567 


6.78 


36 


13.535 


•6.77 


37 


13.505 


6.75 


38 


13.475 


6.74 


39 


13.445 


6.72 


40 


13.420 


6.71 



words curve C (fig. 2) is either the dissociation-residue curve of 
an acid for which log — = 4.8 or the dissociation curve of a base 

for which log— = 9.2 (since 14 - 9.2 = 4.8). 

lVb 

The importance of this relation lies in the fact that a deter- 
mination of the effect of hydrogen ion concentration on some 
process may not reveal whether the phenomenon has to do with 



30 THE DETERMINATION OF HYDROGEN IONS 

an acid or a base, unless an independent method reveals the nature 
of the active substance. 

The student will find it interesting to plot dissociation curves for acids 
with percentage dissociation as one coordinate and pH as the other, and 

then dissociation curves for bases with log .„„_. (which may be called 

pOH) as one of the coordinates plotted inversely as pH. At a given temper- 
ature and given value for K w there is a fixed value for pOH at each value 
for pH. This follows directly from equation (6) ; and it is particularly to 
be noted that in deriving this relation we need not fix the position of the 
pOH scale in its relation to the pH scale by confining our attention to the 
special case where [H + ] = [OH - ], occurring roughly at pH 7.0. Indeed the 
so-called neutral point (pH 7.0) may be considered only as a convenient, 
mental reference point having comparatively little physical significance. 
It is not the point to which titrations are led, except under the rare con- 
dition that the acid and the base are of exactly equal strength; and it is 
of far less importance for amphoteric electrolytes than is the isoelectric 
point of the given ampholyte. 

Having plotted the two systems mentioned above the student will find 
it interesting to assume that for moderate variations of temperature the 
dissociation constants of acids and bases do not change seriously, and then 
to note the shift in the two systems relative to one another when K w is 
altered with temperature. 

The treatment accorded simple acids and bases may be ex- 
tended to poly-acidic acids and poly-basic bases as well as to 
those compounds containing both acidic and basic groups which 
are called amphoteric electrolytes. It seems to be true very often 
for such compounds that they dissociate in steps as is illustrated 
in the titration curve of the tri-acidic phosphoric acid shown on 
page 41. In this, as in many other cases, the several dissocia- 
tion constants are of such widely different magnitudes that, when 
we plot the dissociation curves as if of separate acids possessing 
these dissociation constants, the curves do not seriously overlap. 

Such acids may therefore be treated as if composed of two or 
more independent acids. The effect produced when two dissocia- 
tion constants lie closer together is illustrated by the titration curve 
of o-phthalic acid shown on page 273. If in this case the formal 
dissociation curve of a simple acid be plotted over the main 
position of each section of the phthalate curve, it will be found 
(as shown by Acree) that the experimental curve follows very 
closely the interpolated resultant of the two formal single curves. 



GENERAL RELATIONS AMONG ACIDS AND BASES 



31 



For amphoteric electrolytes (i.e., electrolytes containing acidic 
and basic groups) a relation of great importance to protein chem- 
istry may be illustrated by -the conduct of the simple ampholyte, 
p-amino benzoic acid. The acid dissociation constant K a is 
6.8 X 10~ 6 and the basic dissociation constant K b is 2.3 X 10 -12 
(Scudder). Translating these into the corresponding pH values 
we have 5.17 and 2.36. If we regard the compound as if it were 
made up of an acid and a base with the above dissociation con- 




Fig. 3. Dissociation and Dissociation-Residue Curves op p-Amino- 

benzoic Acid 
Treated as if the amphoteric electrolyte were composed of an acid of 

log — = 5.17 and a base of log — = log — — — 2.36. 
K a Kb K w 



stants (in terms of pH) and each independent of the other, we 
can plot the dissociation curves of each with the aid of equations 
(10 and 14). In each case the dissociation-residue curves are the 
complements. These are plotted in figure 3 with heavy lines. 
It is seen that they cross at pH = 3.77. This means that at 
pH = 3.77 there is a maximum of undissociated residue. Now 
if the salts are more soluble than the free compound itself there 
should be a minimum solubility at pH 3.77. Michaelis and David- 
sohn (1910) found a minimum solubility at pH 3.80. 

Turning again to the light lines A and B of figure 3, we see that 
their intersection is at a point where the percentage of the com- 



32 THE DETERMINATION OF HYDROGEN IONS 

pound ionized as an anion is equal to the percentage ionized as 
a cation. In other words the amount carrying a negative charge 
is equal to the amount carrying a positive charge. Because of 
this equality the point where it occurs is called the isoelectric 
point. 

If we still maintain the simple conditions postulated in this 
elementary treatment, we can calculate the isoelectric point from 
the dissociation constants of an amphoteric electrolyte. 

Consider an amphoteric electrolyte of the type HROH for 
which we have the following equilibrium equations: 

[HR+] [OH- 



[HROH] 
[ROB] [H+] 



= K b (15) 

- K a (16) 



[HROH] 

When [HR+] = [ROH] (isoelectric condition) 

[HROH] _ [HROH] 
b [OH-] " a [H+] 

Hence [H+] - W— K (17) 

"Kb 

In the case cited above [H+] = W '^ — •— ; 10 -14 



2.3 X10- 12 



or pH = log ^— = 3.77 

P * [H+ 



Furthermore from equations (15) and (16) 

[HR+] + [ROH-] - K b [HROHHH3 + [HROH] 

K w lH+] 

If we let [HR+] + [ROH - ] = X, X becomes a minimum when 



0, a condition fulfilled when [H+] = J^ K, 



d [H+] ' L J IK 

In other words the sum of the anion and cation concentrations 
is a minimum at the isoelectric point. 

Only in case K a = Kb will the isoelectric point correspond with 
the "neutral point." 



GENERAL RELATIONS AMONG ACIDS AND BASES 33 

It is at once evident that the isoelectric point of an amphoteric 
electrolyte is a point at or near which there should tend to occur 
maximal or minimal properties of its solution. Indeed at such 
points have been found to occur minimum solubilities, minimum 
viscosities, minimum swelling, optimum agglutinations, etc. 

It should be emphasized that the foregoing relationships have 
been developed from very simple conditions. When these con- 
ditions have been approached experimental verification has been 
found. The insight thus gained has led to a better understanding 
of complex ampholytes, the complete equilibria of which can 
be seen only in broad outline. In attempting to formulate 
more precisely the equilibrium equations which hold under more 
complex conditions than those postulated above, Michaelis (1920) 
has started with the influence of uni-univalent salts upon a simple 
ampholyte and has then extended his propositions to cover the 
influence of divalent ions and the influence of micelle formation. 
It is of special interest to note that he can account for the dis- 
placement of the precipitation optimum from the isoelectric 
point by the influence of salts and that he finds it necessary to 
caution against considering the isoelectric point to be always 
identical with the point of maximum dissociation residue. He 
also outlines the direction in which various relations will be 
modified by the aggregation of the undissociated ampholyte 
into micelles. 

SUPPLEMENTARY REFERENCES 

Texts on the principles of electrolytic dissociation : LeBlanc, Jones, Nernst, 

Ostwald, Stieglitz (1917). 
Generalized relations among acids and bases: Henderson (1908), Michaelis 

(1914, 1922), S0rensen (1912). 



CHAPTER II 

Some Special Aspects of Acid-Base Equilibria 

Words are the footsteps of reason. — Francis Bacon. 

In the foregoing chapter we have outlined the chief aspects of 
acid-base equilibria. We now have to discuss in more detail 
some of the terminology of special use in acid-base studies and 
also certain important matters which are continually met in 
dealing with that class of electrolytes called the "strongly dis- 
sociating" acids, bases and salts. 

THE pH SCALE 

v When "acidity" was resolved into its two components the nor- 
mality unit was retained for each. As a normal solution of an 
acid had been defined as one containing in 1 litre of solution the 
equivalent of 1 gram atom of acidic hydrogen, so the normal solu- 
tion of the hydrogen ion was defined to be one containing in 1 
litre of solution 1 gram atom of hydrogen ions. 1 

To distinguish between these two components with their com- 
mon unit it has been suggested that we call "normality" in its 
older sense the quantity factor of "acidity" and the hydrogen ion 
concentration the intensity factor. This may serve to emphasize 
a distinction, but the suggested analogy with the quantity and 
intensity factors of energy is confusing when we retain for each 
a unit of the same category. Nevertheless the two components 
remain in a restricted sense the quantity and intensity factors of 
"acidity." The one is the total quantity of available acid. The 
second, the concentration of the hydrogen ions, represents the 
real intensity of "acidity" whenever it is the hydrogen ion which 
is the more directly active participant in a reaction. This is 
admirably expressed when we use for hydrogen ion concentrations 
a mode of expression which links it with the potential of a hydro- 
gen electrode. It so happens that in determining the hydrogen 

1 It makes little difference whether the atomic weight of hydrogen be 
taken as 1.008 or as 1.0 in calculating [H + ]. 

34- 



SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 35 

ion concentration with the hydrogen electrode the potentials of 
this electrode are put into an equation which reduces to the 
form : 

Potential , 1 

= log 



lo g frr+i tne symbol P H + 



Numerical factor [H+l 

Thus log r7jqT is at once obtained by the most simple of calcula- 
tions. S0rensen (1909) saw that this value serves to define a 
hydrogen ion concentration quite as well as [H + ] itself and in his 
Enzyme Studies' II, he used this mode of expression and gave to 

[H- 

As a matter of typographical convenience 2 we shall adopt pH 
in place of P H + . Since this is coming into wide usage its uniform 
adoption is recommended in place of the bothersome variations 3 
which have made their way into the literature. 

Although S0rensen has not revealed the considerations which 
led to the choice of the letter P in his symbol, we might regard P 
as suggesting the potential (intensity) factor of acidity in the 
sense described above. 

Writing the potential equation given on page 154 as 

W = EF = RTln =tj 
*At*. [H+] 

it will be seen thatuE is the intensity factor in the work required 
to carry a gram atom of hydrogen ions from concentration [H + ] 
to concentration 1 normal; and pH is a linear function of E. 

pH is sometimes called the S0rensen value or S0rensen unit 
and following S0rensen's original suggestion it is named the 
hydrogen ion exponent. The last mentioned name must be used 
with some caution because of a difference in sign between a 
given pH value and the exponent occuring when the normality 
of the corresponding hydrogen ion concentration is written. For 

2 As is the custom of the Journal of Biological Chemistry. 
J 3 Certain punctilious authors have insisted that the original symbol 
should be retained but have made the mistake of assuming it to be P H - 
The following variations are found in the literature: 

ph,pH,Ph,PH,Ph,P H ,Ph,PH, also each case italicised. 



36 THE DETERMINATION OF HYDROGEN IONS 

examples — 7 is the exponent in 10 -7 , but the pH value correspond- 
ing to [H+] = 10- 7 n is +7. 

The convenience of pH over [H+] is manifest when we compare 
the numerical values encountered in chemical and physiological 
studies. For instance, one enzyme may operate most actively at 
a hydrogen ion concentration of 0.01 normal while another is 
most active at 0.000,000,001 normal. While convenient abbre- 
viations of such unwieldy values are 1 X 10~ 3 and 1 X 10~ 9 , 
there remains the difficulty of plotting such values on ordinary 
cross-section paper. If the difference between 0.000,000,001 and 
0.000,000,002 is given a length of one millimeter, the difference 
0.01 to 0.02 when plotted on the same scale would be ten kilo- 
meters, ten kilometers distant. Evidently the logarithmic 
spacing should be followed and fortunately it is the log- 
arithmic plotting of hydrogen ion concentration (in terms of 
pH) which correctly depicts the fact that the difference between 
1 x 10 -9 and 2 x 10 -9 may be as important for one set of 
equilibria as the enormously greater difference between 1 X 10 _J 
and 2 X 10 -2 is for another set of equilibria. This is revealed 
in the charts on previous and subsequent pages. 

Thus both convenience and the nature of the physical facts 
compel us directly or indirectly to operate with some logarithmic 
function of [H + ]. 

It is unfortunate that a mode of expression so well adapted to the treat- 
ment of various relations should conflict with a mental habit. [H + ] repre- 
sents the hydrogen ion concentration, the quantity usually thought of in 
conversation when we speak of increases or decreases in acidity. pH varies 
inversely as [H + ]. This is confusing. 

The normality mode of expression has historical priority and conse- 
quently conventional force. Since there is a hydrogen ion concentration 
for each hydroxyl ion concentration it became the custom, following Fried- 
enthal (1904), to express both acidities and alkalinities in terms of [H + ], 
This gave a scale of one denomination and the meaning of "higher" and 
of "lower" became firmly fixed. Now we meet the new scale with its direc- 
tion reversed. The inconvenience is unquestionable and very largely be- 
cause of it the pH scale has been criticized. 

See the discussion in the Journal of the Washington Academy of Sciences 
by Wherry and Adams (1921) and by Clark (1921). Wherry's (1919) chief 
object is to establish a scale of convenient direction but in doing so he 
gains a superficial advantage at the expense of several simple and very 
important experimental and theoretical relations which he has not taken 
into consideration. 



SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 



37 



In Chapter XIX there will be advanced a reason for adhering 
to the use of the pH introduced by S0rensen; but at this point it 
may be well to say that in both of the two chief methods of deter- 
mining hydrogen ion concentration we encounter physical rela- 
tions which make the errors proportional to pH rather than 
to [H + ]. Furthermore, pH is the more directly related to certain 
electrode phenomena which are partially dependent upon hydro- 
gen ion concentration and therefore pH is useful in dealing with 
subjects outside the strict limits of hydrogen electrode 
measurements. 

The gross relation of [H+] to pH is shown in the following table. 
See also table B appendix. 



/ r 



[H+] 


pH 


[H+] 


pH 


io-° 





lO" 8 


8 


lO" 1 


1 


10" 9 


9 


10" 2 


2 


10 -io 


10 


io-» 


3 


10" 11 


11 


io-« 


4 


10 "12 


12 


io-« 


5 


10~ 13 


13 


io-« 


6 


10~ 14 


14 


10" T 


7 







The following symbols indicating hydrogen ion concentration 



in normality are encountered in the literature [H+]; [H' 

C H ;h. 



j n 



s. 



THE EFFECT OF DILUTION 



A litre of normal acid becomes a fifth normal solution if diluted 
to 5 litres; the hydrogen ion concentration may in many instances 
be affected too little for the change to be detected by any but 
refined methods. This apparent anomaly is frequently encoun- 
tered and sometimes advantage of it is taken in the dilution of 
solutions otherwise too dense optically for the application of the 
indicator method. The effect of dilution upon the hydrogen ion 
concentration of a solution may be briefly generalized by some 
approximations. 



38 THE DETERMINATION OF HYDROGEN IONS 

Consider an acid of the type HA for the dissociation of which 
we have the equilibrium equation: 

[H+] X [A~] _ 
[HA] 

If K a is small there must obviously be a large reserve of undis- 
sociated acid so long as the concentration of total acid is high. 
As the solution is diluted this reserve dissociates to keep K a 
constant; but there is a readjustment of all components which 
can be conveniently followed only by means of the simple algebraic 
equation expressing the equilibrium condition. 

If the acid alone is present in the solution we may assume that 
[Ai = [H+]. Also if S a = the total acid, [HA] = S a - [H+]. 

Substituting these in the above equation and solving for [H + ] 
we have: 

[H+] = WK a S a + ^--K a (18) 

* 4 2 

When K a is small in relation to S a 

[H + ] S VkK (19) 

Compare the equation on page 19. On these assumptions the 
hydrogen ion concentration should vary with dilution of the 
solution (diminution of S a ) only as the square root of K a S a . 

If there is present a salt of the acid we can apply the equation 
derived on page 24 which shows that the hydrogen ion concen- 
tration of a mixture of a weak acid and its highly dissociated salt 
is determined approximately by the ratio of acid to salt. Since 
dilution does not change the ratio, such a mixture should not suf- 
fer a change of hydrogen ion concentration beyond the narrow 
limits set by the approximate treatment with which this relation 
was derived. 

Therefore, except for solutions of high hydrogen ion concentra- 
tion induced by the presence of unneutralized strong acids, the 
hydrogen ion concentration should vary with dilution somewhere 
between the zero change indicated by the last approximation and 
the square root relation first indicated. 

Such a conclusion takes no account of changes of equilibrium 
which sometimes occur in colloidal solutions. 



SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 



39 



For bases and amphoteric electrolytes similar relations may be 
deduced. One <jr two actual cases may be of interest. 

S0rensen has given the following table of the pH values of dif- 
ferent dilutions of asparagine and glycocoll. 



MOLECULAR CONCEN- 
TRATION OF GLY- 
COCOLL 


pH 


MOLECULAR CONCEN- 
TRATION OF ASPAR- 
AGINE 


pH 


1.0 


6.089 


1.0 


2.954 


0.1 


6.096 


0.1 


2.973 


0.01 


6.155 


0.01 


3.110 


0.001 


6.413 


0.001 


3.521 


0.0001 


6.782 


0.0001 


4.166 



The dilution he're is ten-fold at each step, yet the increase in 
pH is very small while the solutions are beween 1.0-0.01 M. 

Walpole (1914) besides giving data on the hydrogen electrode 
potentials of various dilutions of acetic acid and "standard ace- 
tate," has determined the effect of a twenty-fold dilution of 
various acetic acid-sodium acetate mixtures. The change of pH 
on twenty-fold dilution of standard acetate is about 0.08 pH; 
and of mixtures of acetic acid and sodium acetate which He on 
the flat part of the curve the change of pH is of the same order 

acetic acid 

of magnitude. When the ratio — - -—reaches 19/1 the 

sodium acetate 

change is about 0.3 pH. 



BUFFER ACTION 

If we were to add to 1 liter of perfectly pure water of pH 7.0, 
1 cc. of 0.01n HC1, the resulting solution would be about pH 
5.0 and very toxic to many bacteria. If, on the other hand, we 
were to add this same amount of acid to a liter of a standard beef 
infusion medium of pH 7.0, the resulting change in pH would 
be hardly appreciable. This power of certain solutions to resist 
change in reaction was commented upon by Fernbach and Hubert 
(1900) who likened the resistance of phosphate solutions to a 
"tampon." The word was adopted by S0rensen (1909) and in 
the German rendition of his paper it became " Puffer" and thence 
the English "buffer." There has been some objection to this 



40 THE DETERMINATION OF HYDROGEN IONS 

word so applied but it now possesses a clear technical meaning and 
I is generally used. By buffer action we mean t£e resistance ex- 
hibited by a solution to change in pH through the addition or loss 
of acid or alkali. This may be illustrated by titration curves such 
as those shown in figures 4, 5 and 6. The construction of such 
curves may be illustrated by the following example. 

A 1 per cent solution of Witte peptone was found to have a 
pH value of 6.87. To equal portions of the solution were added 
successively increasing amounts of O.In lactic acid and the result- 
ing pH was measured in each case. There were also added to 
equal portions of the solution successively increasing amounts of 
O.In NaOH and the resulting pH was measured in each case. 
The pH values were then plotted on cross section paper as ordi- 
nates against the amount of acid or alkali added in each case as 
abscissas. This gave curve 1 shown in figure 4. The other 
curve shown in this figure was constructed with data obtained 
with a 5 per cent solution of Witte peptone. The curves of fig- 
ures 5 and 6 were obtained in a similar way. 

These curves illustrate the following points. 
' Figure 4 shows that the buffer action of a solution is dependent 
upon the concentration of the constituents. The 5 per cent solu- 
tion is much more resistant to change in pH than the 1 per cent 
solution. It will also be noticed that in either case the buffer 
action is not the same at all points in the curve. In other words 
the buffer action can not be expressed by a constant but must 
be determined for each region of pH. This is illustrated even 
more clearly by the titration curve for phosphoric acid (fig. 5). 
At the point where the solution contains only tha:primary phos- 
phate and again where it contains only the secondary phosphate 
there is very little buffer effect indeed. 

Furthermore the buffer action of a solution may not be due 
entirely to the nature of the constituents titrated but also to. the 
nature of the substance with which it is titrated. This point 
may be illustrated by titrating a beef infusion medium in the one 
case with hydrochloric acid and in the other case with lactic acid, 
both of the same normality (see fig. 6). It will be seen that at 
first the two curves are identical. As the region is approached 
where the dissociation of the "weak" lactic acid is itself sup- 
pressed because of the accumulation of lactate ions and the high 



SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 



41 





















A 








































^ 














































































■ 5 


•7 






































e 


/ 


<*/ 


































O 


/ 






































T 


k 














































































% 








































r 






































/ 


r» 


X 




































/ 


j 






































/ 


























A 








2 


> 






c 


) 






r 


\ 






4 





c.c. 

Fig. 4. Titration Curves of 1 Per Cent and 5 Per Cent Peptone 

Ten cubic centimeters of peptone solution titrated with N/10 lactic acid 
(to right) and with N/10 NaOH (to left). 





i!£5 






























































4 










\ 






























' 


foyi 


Si 






























V 




















6 
































































































10 
P H 






















KjHP 


\ 




























V 






































W 



c.c. 



50 



100 



150 



Fig. 5. Titration Curve of Phosphoric Acid 
Fifty cubic centimeters M/10 H 3 P0 4 titrated with N/10 KOH. 



42 



THE DETERMINATION OF HYDROGEN IONS 



concentration of the hydrogen ions, further addition of this acid 
has comparatively little effect. The strong hydrochloric acid 
on the other hand continues to be effective until its dissociation, 
too, at very high hydrogen ion concentrations is suppressed. 



P H 



8 























f> 




























LA 


cue. 

















































c.c. 



20 



40 



60 



Fig. 6. Titration Curves op a Beep Infusion Medium 

One hundred cubic centimeters medium titrated with N/5 HC1 and with 
N/5 lactic acid. 

These examples will suffice to make it evident that the buffer 
action of a solution is dependent upon the nature and the concen- 
tration of the constituents, upon the pH region where the buffer 
action is measured and upon the nature of the acid or alkali 
added. To connect all these variables is a difficult problem. 
Koppel and Spiro (1914) have attempted to do so but they have 
necessarily had to leave out of consideration another factor. If 



SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 43 

there are present any bodies which tend to adsorb any of the con- 
stituents of a solution which can affect the hydrogen ion concen- 
tration of a solution, these bodies will tend to act as buffers or 
will affect the buffer action of the solution. Henderson (1909) has 
called attention to this and Bovie (1915) has shown in a very 
interesting way the buffer action of charcoal. Since some culture 
media or cultures and many of the solutions whose buffer action 
must be studied for physiological purposes, contain undissolved or 
colloidal material which may act in this way, it seems best to 
consider buffer action in its broadest sense, and to express it by 
the relative slopes of titration curves determined experimentally. 
Further illustrations of titration curves of culture media will be 
found in the papers of Clark (1915) and of Bovie (1915). Titra- 
tion curves of some inorganic solutions will be found in a paper 
by Hildebrand (1913). 

The reader will have perceived the elementary theory under- 
lying buffer action. The titration curve of phosphoric acid (fig. 5) 
illustrates the principles discussed on previous pages. The titra- 
tion curve of a "peptone" solution integrates as it were the effects 
of acids, bases and ampholytes, in complex mixture. 

Returning to figure 1 we see that along the flat portion of the 
curve considerable alkali has to be added to produce much change 
in pH. Conversely, the addition of a strong acid would not have 
anywhere near the effect at this flat portion of the curve that it 
would have near either end. Thus it is evident that a mixture of 
a single acid and its salt will tend to stablize the pH of the solution 
only within a certain narrow zone having vague boundaries. 
Mixtures buffering the solution within such a pH zone are often 
referred to as "regulator mixtures." They are of very great 
value to the analyst and the physiological chemist in that they 
furnish a means of stablizing the hydrogen ion concentration 
within a predetermined zone. The middle point of this zone, 
where the strongest buffer action is exerted, is determined approxi- 
mately as shown on page 25 by the dissociation constant of the 
acid or base concerned. Other things being equal the choice of 
mixtures is thus revealed in a table of dissociation constants. 
* [ More theoretical treatments of the subject are given in the 
papers of Henderson (1909), S0rensen (1909), S0rensen (1912), 
Michaelis (1914) and Koppel and Spiro (1914). 



44 THE DETERMINATION OF HYDROGEN IONS 

Unless a solution is buffered to some extent in some way, it is 
almost impossible to make an accurate electrometric determina- 
tion of the pH; and because of the influence of traces of carbon 
dioxid and other acidic or basic contaminations such solutions 
may be very unsuitable when used for physiological purposes. 
Thus the failure to buffer against the effect of so-called neutral 
salts which are not truly neutral may lead to gross error. In like 
manner the failure to buffer has rendered physiologically unstable 
certain so-called synthetic and supposedly stable culture media. 

In the preparation of standard buffer mixtures it is of course, preferable 
to use a high grade of water if accuracy is required but there is little need 
of carrying this to an extreme. "Conductivity water" is sometimes speci- 
fied for the preparation of special standards because the ordinary distilled 
water of certain regions of the country is such that "distilled water" means 
nothing. The exercise of judgment is advantageous. 

The maintenance of "neutrality" by such solid reagents as calcium car- 
bonate may be considered as a buffer action. It is very important to note 
however that the use of calcium carbonate may become a grossly inefficient 
procedure. To show its inefficiency the author has placed at the bottom of 
a test tube a deep layer of very finely divided, freshly precipitated and well 
washed calcium carbonate and overlaid this with cultures of bacteria and 
molds in sugar media. Indicators show that unless the calcium carbonate 
is frequently and thoroughly shaken with the medium only the solution 
in direct contact with the calcium carbonate is neutralized. Molds may 
develop an acidity as high as pH 2 within a few millimeters of the carbonate. 

THE CONDUCT OF STRONG ELECTROLYTES 

The relations set forth in the preceding pages, even in the 
approximate form adopted to keep the distinctive lines of the 
picture clear, afford in their experimental verification the best of 
evidence that the theory of electrolytic dissociation is essentially 
correct. That it is incomplete is shown when we turn to the 
examination of the quantitative data for strong electrolytes — 
acids such as hydrochloric and nitric and salts such as the simple 
chlorides. For instance, if the conductance of a solution is 
ascribed to the concentration and the mobilities of the ions, and 
if the mobilities be considered constant at all dilutions, the con- 
ductance data should satisfy the Ostwald dilution law and furnish 

a dissociation constant. The Ostwald dilution law is q _ a ) v = * 



SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 45 

where a is the degree of dissociation, v the dilution and k the 
equilibrium constant which should be independent of the dilution; 
a should be equal to the ratio of equivalent conductance at dilu- 
tion v to equivalent conductance calculated for infinite dilution. 
For potassium chloride, k varies from 0.049 at 1000 dilution to 
0.541 at 10 dilution. The discrepancies with hydrochloric acid 
are comparable. 

The reader will recall that in the derivation of the equilibrium 
constant (page 19) there was introduced an assumption full of 
danger. The assumption was that the physical environment, 
within which occur the reactions of dissociation and recombination, 
remain constant. It has already been mentioned that a change 
in temperature changes the equilibrium constant and that a 
change in solvent produces a more profound effect. Now it is 
not at all improbable that the presence of relatively large concen- 
trations of ions and especially of the hydrogen or hydroxyl ions 
constitutes an environment appreciably different from that of a 
dilute solution. If so, we should hardly expect to find an equilib- 
rium constant holding over a great range of concentration. Yet 
it is by changing concentration that we expect to so alter the 
distribution of "species" that we may demonstrate the "mass" 
law experimentally. 

But there are other possible difficulties. For instance, data 
upon what may be called the structure of solutions, the mutual 
influence of solvent and solute upon association of solvent mole- 
cules, association of solute molecules and association of solvent 
with solute are still hazy. Furthermore it is difficult to say 
what degree of separation constitutes ionization as measured by 
different methods. Therefore it is impossible to give rigidly 
accurate values to the concentrations of active molecules. When, 
therefore, it is stated that the anomalies of strong electrolytes 
"disprove the mass law," it may be only a clumsy way of saying 
that we do not know how to give the case an adequate test. 

To give any adequate review of the present status of the prob- 
lem would require undue space A most valuable review ap- 
peared in the discussions which took place in the Faraday Society 
and which are published in the December, 1919, number of the 
Transactions. It is there made very evident that the " anomalies " 
of strong electrolytes have been the bugbear of students of ioni- 



46 THE DETERMINATION OP HYDROGEN IONS 

zation, have stimulated most brilliant researches and promise to 
be the starting point for new developments which will harmonize 
the entire body of data. 

There have been attempts to formulate the facts by means of 
purely empirical equations; and then again the pendulum has 
swung back to a faith that the original simple assumptions could 
be satisfied if interfering factors were discovered and their numeri- 
cal magnitudes introduced as corrections. More recently there has 
come to the fore the "activity" concept of Lewis. This will be 
mentioned again in Chapter XIX. This concept has attained con- 
siderable success in systematizing the data; but whether it will 
have an appeal universal enough to satisfy minds of the type of 
Lord Kelvin, which reason not only in abstract terms but also 
demand concrete models, remains to be seen. 

When there occur in the development of a science such baffling 
difficulties as have arisen in the case of "strong electrolytes," 
it is highly desirable to abandon both complex reasoning and end- 
less corrections, if an entirely new basis can be found. This 
statement will appear gratuitous or even foolish to those who are 
so possessed with the idea of the complexity of aqueous solutions 
that they admit no theory as sufficient that is not itself complex; 
but the history of other developments has shown that in the face 
of similar complexities a simple basis of reference has been found 
and has won acceptance through its convenience. 

Whatever may be the opinion of the reader he will doubtless 
agree that we are in the midst of or at the beginning of a period 
of transition, and that it is incumbent upon the experimenter to 
keep his data as free as is convenient from confusions introduced 
by tacit assumptions. In the following treatment of our subject 
assumptions common to the age will remain, but at least they will 
be more clearly recognized than if we straddled the issue that has 
arisen. We shall therefore proceed with the concept of "con- 
centration" as commonly used, since it is the more convenient 
for elementary descriptive text. Finally in Chapter XIX we shall 
redefine certain standards in such a way as to embody current 
procedures and at the same time relieve the biochemist from 
embarrassments due to the present state of flux. 

Although free acidities of a magnitude that fall within the 
grosser uncertainties of our knowledge of strong electrolytes are 



SPECIAL ASPECTS OF ACID-BASE EQUILIBRIA 47 

seldom met in physiological solutions, the whole system of pH 
measurements is scaled from certain assumptions regarding the 
now uncertain conduct of HC1 as will be shown in Chapter XIX. 
Furthermore we have continually to deal with solutions contain- 
ing salts whose conduct is so little understood that precise treat- 
ment is impossible. This will appear in the so-called salt error of 
indicators and the strange fact that the apparent hydrogen ion 
concentration as determined with the hydrogen electrode may be 
raised above the quantity of available acid present by the addi- 
tion of sufficient salt. To deal with such questions without trac- 
ing back through the subtleties of certain tacit assumptions is a 
most pernicious practice. It seems wiser to admit at once that 
certain of the more fundamental assumptions are too insecurely 
based to provide any adequate systematic treatment at the present 
time, and for this reason such questions as the salt error of indi- 
cators will be given in the subsequent chapters what may at first 
appear to be too brief a treatment. Experimentally the safest 
procedure to follow whenever the conduct of strong electrolytes 
enters into the determination of or the use of pH values is stand- 
ardization of data. 

Standardization of experimental data on the one hand and the 
maintenance of the more simple concepts of the theory of electro- 
lytic dissociation will then be the policy of the following treatment. 

SUPPLEMENTARY REFERENCES 

A few references on the conduct of "strong electrolytes" and the "activity" 
concept. Arrhenius (1887, 1914), Beattie (1920), Bjerrum (1919), 
Bronsted (1919-1922), Ebert (1921,)* Ferguson (1916), Ferguson- 
France (1921), Getman (1920), Ghosh (1921), Harkins (1920), Harned 
(1916, 1920, 1922), Hill (1921), Jahn (1900), Kendall (1921, 1922), 
Kraus (1920, 1921), Lapworth (1915), Lewis (1907-1922), Linhart (1917, 
1919), Noyes (1907), Noyes-Maclnnes (1920), Maclnnes (1919), 
Rabinowitsch (1921), Stern (1922). Symposium on theory of electro- 
lytic dissociation Trans. Faraday Society 15, 1-178, Dec. 1919. 

pH calculator. Klopsteg (1921). 

pH tables and graphs. Appendix table b. Matula (1916), Roaf (1920), 
Schmidt-Hoagland (1919), Symes (1916). 

* Contains extensive review. 



CHAPTER III 

Outline op a Colorimetric Method 

Acidimetric-alkalimetric indicators are substances, the colors 
of which correlate with the hydrogen ion concentrations of the 
i aqueous solutions in which they are dissolved. 

For each indicator there is a characteristic pH zone. On the 
acid side of this zone the indicator is completely transformed into 
its "acid color" and on the alkaline side of this zone the indicator 
is completely transformed into its "alkaline color." Within the 
characteristic pH zone there may be observed different proportions 
of the acid and alkaline colors. 

In ordinary titrations conditions are so chosen that when the 
"end-point" of the titration is reached the pH of the solution 
passes suddenly through the whole range of the indicator's color- 
change. The intermediate stages, if observed, are not emphasized. 
The intermediate colors, however, are the important ones for the 
present purpose. They can be maintained with buffer solutions; 
and, being characteristic at definite pH values, they can be used 
to estimate the pH of tested solutions by a system of comparison 
with standards. To distinguish the stabilized degree of color 
transformation from the changing color observed during a titra- 
. tion, we shall adopt S0rensen's term and speak of the virage of 
an indicator when referring to a particular, stabilized degree of 
color transformation. 

For reasons which will be given in Chapter IV the characteristic 
pH zone, within which differences of virage may be observed, is 
comparatively narrow. It is therefore necessary to have a series 
of indicators, the zones of which overlap (see table on page 80). 
Then if an indicator is found to be transformed completely to its 
acid color by a solution under test, the indicator next in the series 
is tried and so on until there is found the indicator which is trans- 
formed by the solution 'to an intermediate virage. It is then 
known that the solution has a pH value within the limits char- 
acteristic of the indicator used. 

For some purposes it is sufficient to know the approximate pH 
and this may be estimated from the degree of color transformation 

48 



OUTLINE OF COLORIMETRIC METHOD 49 

induced in the indicator. It is a simple matter, however, to take 
the first step toward accuracy. This is done as follows. 

There have been determined by hydrogen-electrode methods 
the pH values of definite buffer solutions such as mixtures of 
KH2PO4 and Na 2 HP04. Series of such solutions and the details 
of their preparation are described in Chapter VI. By adding 
definite quantities of an indicator to definite volumes of these 
standard solutions a series of color standards is easily prepared. 
With these standards the color of the tested solution can be 
compared. For instance, suppose that the preliminary test of a 
given solution has shown that it transforms the indicator phenol 
red neither to a full red nor to a bright yellow but that the pro- 
portion of red is low. Previous experience has impressed the fact 
that such a virage with phenol red indicates the solution to be near 
pH 7.0. See the color chart. Therefore, one employs those 
standard buffer solutions giving pH values near 7.0. To a series 
Df uniform test tubes is added seriatim 10 cc. of each of the 
standard phosphate solutions described in Chapter VI. To each 
:ube is added five drops of phenol red solution. On mixing there 
vill be observed a graded series of virages and perhaps three of 
;hem will be recognized at once to have nearly the same color as 
10 cc. of the tested solution mixed with 5 drops of the same indi- 
;ator solution. When closer inspection shows where the color- 
natch occurs, the standard with its known pH value and the 
ested solution are supposed to have the same pH value. As in 
his example, it is always necessary to make comparisons between 
,ike concentrations of indicator viewed through equal depths of 
s olution. 

Anerrorjnay be made if the standard and tested solutions / 
i liffer much in total salt concentration, or if the tested solution 
i ontains much protein, or if an unreliable indicator is used. But 
\ fe shall have to deal with these and other difficulties in subse- 
( uent chapters. 

When one is familiar with the virages of the indicators at 
] nown pH values very fair estimations may be made without the 
i id of the standards; but there is no way as satisfactory as the 
{ stting up of the standards for the establishment of a correct 
i npression of the relations of the various indicators on the pH 



50 THE DETERMINATION OF HYDROGEN IONS 

scale. On the other hand, the author has discovered in his 
conversations that there are a great many investigators who 
would like to use indicators for the occasional rough measurement 
of pH but who are discouraged by a pressure of work which pre- 
vents them from taking the time to carefully prepare the standard 
solutions. To furnish such investigators with a demonstration of 
the general relations of the various indicators and to furnish 
rough standards the attempt has been made in figure 8, to repro- 
duce the colors. The colors of standard buffer solutions con- 
taining definite quantities of the several indicators were reproduced 
very faithfully by Mr. Max Broedel of the Johns Hopkins Medical 
School. It must be remembered, however, that in undertaking a 
second reproduction by means of the printer's art the publishers 
are to be commended for their courage and are not to be held 
responsible for the inadequacy of the result. Aside from the 
inherent difficulty in freeing a printed color from the effect of the 
vehicle, there remains the utter impossibility of reproducing upon 
paper the exact virage observed in a liquid solution. The funda- 
mental phenomena are quantitatively very different in the two 
cases. Therefore the user of the chart of colors will have to use 
discretion and some imagination. If he does not attempt to 
make the reproductions take the place of the standards he should 
find them useful for class room demonstrations, for refreshing the 
memory and for rough standards. 1 

In each case the colors were reproduced from tubes 16 mm. 
internal diameter containing 10 cc. standard buffer solution. 
The quantities of indicator solution added in each case were as 
follows: Thymol blue, acid range (T. B. acid range) 1 cc. 0.04 
per cent solution. Brom phenol blue (B. P. B.) 0.5 cc. 0.04 per 
cent solution. Methyl red (M. R.) 0.3 cc. 0.02 per cent solution. 
Brom cresol purple (B. C. P.) 0.5 cc. 0.04 per cent solution. Brom 
thymol blue (B. T. B.) 0.5 cc. 0.04 per cent solution. Phenol red 
(P. R.) 0.5 cc. 0.02 per cent solution. Cresol red (C. R.) 0.5 cc. 
0.02 per cent solution. Thymol blue (T. B.) 0.5 cc. 0.04 per cent 
solution. 

1 Separates of the color chart may be obtained from the publisher. 



Dr. Barnett Cohen of the Hygienic Laboratory has recently 
(Public Health Reports, U. S. P. H. S., 38, 199, 1923) synthe- 
sized the following new sulfonphthalein. Brom cresol green 
covers the range of methyl red. Salt and protein errors have 
not yet been determined. 



CHEMICAL, NAME 


8CGGESTED COMMON NAME 


APPARENT 

DISSOCIATION 

CONSTANT 


pH 

RANGE 


m-Cresol sulfonphthalein 


Meta cresol purple 


2.8 X lO" 2 
5.0 X 10~ 9 


0.5-2.5 
7.6-9.2 


Dibromo-dichloro-phenol sul- 
fonphthalein 
Tetra bromo-m-cresol sulfon- 


Brom-chlor phenol 

blue 
Brom cresol green 


7.9 X lO" 6 
1.0 X 10~ 5 


3.2-4.8 
4.0-5.6 


phthalein 

Dichloro-phenol sulfonphtha- 
lein 

Dibromo-phenol sulfonphtha- 
lein 


Chlor phenol red 
Brom phenol red 


8.9 X 10~ 7 
4.5 X 10~ 7 


5.0-6.6 
5.4-7.0 



OUTLINE OF COLORIMETRIC METHOD 51 

The ranges of pH covered by the^ several indicators in the 
color chart are: 

T. B. (acid range), Thymol blue 1.2-2.8 

B. P. B., Brom phenol blue 3.0-4.6 

M. R., Methyl red 4.4-6.0 

B. C. P., Brom cresol purple 5.4-7.0 

B. T. B., Brom thymol blue 6.0-7.6 

P. R., Phenol red 6.6-8.2 

C. R., Cresol red 7.2-8.8 

T. B., Thymol blue 8.2-9.8 

For class-room work it is advantageous to show the position 
of the several indicators on the pH scale by relining each series 
so that corresponding pH values overlap. 

One requirement for the colorimetric method is a set of indi- 
cators selected for their relative freedom from the so-called pro- 
tein and salt errors and for their brilliancy. Beside the brilliant 
and reliable selection of Clark and Lubs there is the care- 
fully studied selection of S0rensen given on page 78 with S0rensen's 
summary of properties on page 79. 

There are also required standard buffer solutions whose pH 
values are established from hydrogen electrode measurements. 
It is in the preparation of these standards that the greater part 
of the labor of the colorimetric method is involved ; but, once the 
stock solutions are carefully made, the preparation of the mix- 
tures is a simple matter. If only the pH range 5.2 to 8.0 is 
necessary, the S0rensen mixtures of primary and secondary phos- 
phates are the more convenient. If a wider range is desired the 
system tabulated on pages 106 to 107 is recommended. 

For precise measurements there are required control by hydro- 
gen electrode measurements and constant watchfulness for the 
several sources of error noted in following chapters. Approximate 
methods are described in Chapter VIII. 

In figure 7 are shown several pieces of equipment useful in 
colorimetric work. Beginning at the left is, first, a sample of 
a litre bottle used for holding the standard stock solutions, such 
as M/5 KH Phthalate, which are not seriously affected by expo- 
sure to the carbon dioxide of the laboratory air. In Clark and 
Lubs' series of standards (see page 99) there are required four 
such bottles. In this same series there is required a container for 







C3 - 







6 f 



OUTLINE OF COLORIMETRIC METHOD 53 

standard M/5 NaOH. This should be a paraffined bottle with 
calibrated burette and soda-lime guard-tubes attached. 

In figure 7 there is next shown a comparator whose construc- 
tion is given on page 70. This is used in comparing turbid or 
colored solutions with the standards. When the turbidity of a 
tested solution brings into evidence the dichromatism of an indi- 
cator as described on page 65, the comparator is used with the 
light screen shown at the back of figure 7 and described on page 67. 

For ordinary colorimetric comparisons the test tube rack shown 
in the figure is very useful. The holders are the clips sold at 
stationers for holding rubber stamps. Two forms of dropping 
bottle are next shown and, finally, at the right, two paraffined 
bottles for alkaline standards and two acid resistant bottles for 
acid solution. Of such bottles there are required for the series 
of standards given on pages 106-107 fifty-one bottles and the same 
number of 10 cc. pipettes. The range of pH thus covered is wider 
than that called for in special investigations. The pipettes may 
have their tips broken to allow quicker delivery of solution with- 
out serious violation of volume requirements. S0rensen's stand- 
ards, pages 111-114, are designed so that individual 10 cc. samples 
are made up as required. Larger quantities such as are specified 
in table 21 provide for the occasional test. 



CHAPTER IV 

Theory of Indicators 
Les proprUUs des corps sont les proprUUs des nombres.—T>E Chancotjrtois. 

Indicator theory is a cross-roads where the cultivators of 
distinct fields of science meet. Here comes the organic chemist 
with analyses of plant and animal products, structural formulas 
of synthetic dyes, tautomers and chromophores. Here comes the 
physico-chemist with formulations of electrolytic and tautomeric 
equilibria. Here comes the physicist with the theory of color and 
the instruments of light analysis. And perhaps there will meet 
here the psychologist bringing a clearer description of the sub- 
jective aspect. As a confluence of trade routes may determine the 
growth of a city so the confluence of many specialties may some- 
time lead to a great community of interest where the cross-roads 
of indicator theory once lay. Indicators themselves are not 
particularly unique except that they compel the attention of the 
eye. Through this we are made aware of phenomena of wide 
occurrence. 

According to the inclination of a reviewer one or another of 
the manifold aspects of indicator theory might be emphasized. 
"' We must choose that which is useful to the purpose at hand and 
for the sake of a necessary brevity we must try to include only 
so much as will contribute toward an intelligent use of indicators 
as tools for the determination of hydrogen ion concentration. 

In the first place it may be said that the customary manner of 
using indicators is merely a method of comparison involving little 
if any theory. The conduct of an indicator may be, and generally 
is, ."calibrated" by means of hydrogen electrode measurements. 
It is well to emphasize this uninspiring, matter-of-fact aspect 
because it will remind us that with so much of the fundamental 
theory at hand the employment of theory may lead to a wider 
usefulness of the instruments thus far treated empirically. But 
before this can be done important relationships must be ex- 
pressed definitely in numerical data. How this can be done is 
the immediate problem before us. 

54 



THEORY OF INDICATORS 



55 



The first consistent attempt to bring the conduct of indicators 
into relation with electrolytic dissociation was that of Ostwald 
(1891). .He assumed that indicators are acids or bases the undis- 
sociated molecules of which have a color different from that of their 
dissociation products. If this be so, it is evident that the color 



TABLE 4 
Approximate apparent dissociation constants of indicators 



Phenol sulfon phthalein 

o-Cresol sulfon phthalein 

Thymol sulfon phthalein 

Carvacrol sulfon phthalein 

a-Nap&hol sulfon phthalein 

Tetra bromo phenol sulfon phthalein. 
Di bromo o-cresol sulfon phthalein. . . 

Di bromo thymol sulfon phthalein 

Phenol phthalein 

o-Cresol phthalein 

a-Naphthol phthalein 

Methyl red 

Ethyl red 

Propyl red 

Thymol sulfon phthalein (acid range) . 



K a 



.2 X 10" 
.0 X 10" 



10" 
10" 
10" 

io- 

10" 



.2 X 

X 

3 X 

9 X 

X 

X io- 
X io- 

X 10" 

X io- 

9 X 10- 

X io- 

X 10" 

o x io- 



pK a 



7.9 

8.3 

8.9 

9.0 

8.2 

4.1 

6.3 

7.0 

9.7* 

9.4 

8.4 

5. If 

5.4 

5.4f 

1.7 



* This value is identical with Rosenstein's (1912). 

t In the table published in the Journal of the Washington Academy, 
vol. vi, p. 485, these values for methyl red and propyl red were erroneously 
interchanged. 

Tizard (1910) gives K a = 1.05 X 10" 6 or pK - 4.98 for methyl red 
considered as an acid. 

of an indicator should change with the pH of a solution. exactly 
as the dissociation curves described in Chapter I. If, for in- 
stance, the indicator is an acid, colorless in the undissociated 
form, but colored when dissociated as an anion, then the change 
of color with the hydrogen ion concentration should conform to 
the equation: 



K a + [H+] 



where K a is the dissociation constant of the acid indicator and 
a is the degree of dissociation. Assuming then that such a rela- 



56 



THE DETERMINATION OF HYDROGEN IONS 



tion does hold, let us determine K a for a series of indicators in 
the following way. 

From the above equation when « = §, K a = [H + ]. That is, 
at a hydrogen ion concentration corresponding numerically to the 
dissociation constant, the acid is half dissociated. At such a 
hydrogen ion concentration a colorless-to-red indicator, such as 
phenolphthalein, should show half the available color; and a 
yellow-to-red indicator, such as phenol red, should show the half- 
yellow, half-red state. We can match the half way state of this 
first solution by superimposing two solutions each of a depth 
equal to the first, if we have in one of the superimposed solutions 
only the yellow form and in the other only the red form, each 
concentration equaling half the concentration in the first solution. 
Such an arrangement is shown diagraphically in the following 
figure : 



i 



i 



Alkaline solution (full 
red) 5 drops indicator 



Known pH standard 
10 drops indicator 



Acid solution (full yel- 
low) 5 drops indicator 



Water blank 



We may not know at the beginning at what pH the half trans- 
formation may occur, so we vary the pH of the standard solution 
until a match with our superimposed solutions does occur. Then 
we have found, presumably, the hydrogen ion concentration the 
numerical value of which is the dissociation constant of the 
indicator. Values so obtained by Clark and Lubs (1917) are given 
in table 4. 



THEORY OF INDICATORS 57 

< As indicated in Chapter I the determination of the dissociation 
curve, or of the half transformation point, does not tell us whether 
we are dealing with the dissociation curve of an acid or the disso- 
ciation-residue curve of a base or vice versa. Thus methyl red 
is treated in table 4 as an acid and plotted in figure 9 as if the 
color were associated with the undissociated form. Methyl red 
however could be treated as a base. 
Just as it is convenient to deal with a logarithmic function of 

[H+] so the dissociation constants can be used in the form log — 

This can be designated pK a . 

Gillespie (1920) gives somewhat different values but, since the 
method used in each case was approximate, the table given above, 
as it is^found in the paper by Clark and Lubs (1917) will do for 
purposes of illustration. With the aid of the approximately 
determined apparent dissociation constants we are enabled to 
plot the curves shown in figure 9, which reveal graphically the 
relationships of the various indicators in the series we shall dis- 
cuss. This figure shows at a glance that an indicator of the 
simple type we have assumed has no appreciable dissociation and 
consequently exists in only one colored form at pH values begin- 
ning about 2 points below the half transformation point, while at 
the same distance above this point the indicator is completely 
dissociated and exists only in its second form. Between these 
limits the color changes may be observed. The useful range of 
such an indicator is far less than 4 pH units for optical reasons 
which will be discussed later. 

The illustration (fig. 9) will show how in choosing a set of indi- 
cators it is advantageous to include a sufficient number, if reli- 
able indicators can be found, so that their ranges overlap. It 
shows that each of the indicators, when considered to be of the 
simple type we have assumed, has an equal range. It also shows 
that the half transformation point of each indicator occurs nearer 
one end of the useful range, the useful range being indicated by 
the shaded part of the curve. This aspect will be discussed later. 

It is evident that if the actual color change of an indicator varied 
with pH in accordance with a curve such as those in figure 9, 
and if the true dissociation constant were accurately known, then 
the hydrogen ion concentration of a solution could be determined 



<^- 









1 


/ 


GASTB1 C 

JUICS 






^ 

2 




YEAST 
LIMIT 






3 




WIKES 






4 




CASEIN ISO- 
ELECTRIC PT. 






i^L 






X/C 




6 




•*r" 




ii 


7 










* s, <i* 


^V 


SEA 
WATER 








vl 






^s^ 


10 ^ 










11 


\ 













Z$ „ SO 7S 

% DISSOCIATION 



1^10 HCJ 



B.PARA TYPHI ACCL. 

B. TYPHI Afl«L. 
B.COLI LIMIT 
PBEUMOCOCOTS AGCL. 



M/2 



yiO MH 4 OH 



too 



Fia. 9. Indicator Curves and Significant pH Values. Shading 
Indicates Useful Range 



58 



THEORY OF INDICATORS 59 

by finding the percentage transformation induced in the indicator. 
Indeed the dissociation constants of some few indicators have 
been determined with sufficient accuracy to permit the use of 
this method when the proper means of determining the color 
intensities are used. This will be discussed in Chapter VIII. R 

We have been assuming that thejtheory of indicators may be 
treated in the simple manner originally outlined by Ostwald 
(1891). In his theory it was assumed that the anion of an indi- 
cator acid, for instance, has a color different from that of the 
undissociated molecule. This assumption if unmodified does not 
harmonize with what is known. Researches in the phenomena of 
jtautomerism have shown that when a change in color is observed 
in an indicator solution the change is associated with the forma- 
tion of a new substance which is generally a molecular rearrange- 
ment or so-called "tautomer" of the old. If this color change is 
associated with the transformation of one substance into another, 
how is it that it seems to be controlled by the hydrogen ion con- 
centration of the solution? As Steiglitz (1903) and others have 
pointed out, it is the state of these compounds, their existence in 
a dissociated or undissociated condition, which determines the 
stability of any one form. 

The method of dealing with the tautomeric relations of indi- 
cators is shown by the following quotation from Noyes (1910) : 

We may derive a general expression (as has previously been done by 
Acree, 1907) for the equilibrium-relations of any pair of tautomeric acids 
and their ions. The three fundamental equilibrium equations are as 
follows: 

eaaci.K/. (20) (H+) aid - K * . (21) 

(HIn') " ( (HIn") K »» **" 

2S2-&- (22) 
(HInO Kt ' (22j 

Multiplying (21) bv (22), adding (20) to the product, and substituting in 

♦ t ,ttt rx -, , (HlnQ + (HIn' 

tor for (HIn ) its value — 

1 + K T 

(H+) [(In'") + (In'")] K', + K", K, 



fTTTnM -I- fTTTn'M 

the denominator for (HIn') its value — — — given by (22), we get 

1 + K T 



(HInO •+ (HIn") 1 + K, 



= K IA (23) 



If the indicator is a base existing as the two tautomeric substances 
fn'OH and In"OH, having ionization constants K' r and K"i and a tau- 
tomer constant K T denned by equations analogous to (20), (21) and (22), the 



60 THE DETERMINATION OF HYDROGEN IONS 

general expression for the equilibrium between the ionized bases and their 
ions is: 

(OH") [(In'+) + (In y +)] -K'x+K'xKt 



(In' OH) + (In'OH) 1 + K T 



= K IB (24) 



In these expressions a single constant K IA or K IB has been introduced in 
place of the function of the three constants K' x , K"i, and K T . . . • 
The constant so calculated for a pair of tautomeric acids or bases can evi- 
dently be substituted for the ionization constant of an ordinary (non tau- 
tomeric) acid in any derived expression, provided the sum of the two ion 
concentrations and the sum of the two acid or base concentrations are quan- 
tities that are to be known or are to be calculated. 

If then in equation (23) we substitute (In - ) for [(In'~~) -+- (In"~)] and 
(HIn) for [(HIn') + (HIn")] we have: 

(HIn) " KlA (25) 

Applying to Noyes' equation (25) the derivation given on page 25 
we have 

K IA + (H+)' 

From this we may plot the curves of figure 9. Such curves will 
then represent the color transformations when and only when 
(In - ) is substantially equal to (In' - ) or to (In" - ), whichever 
tautomer is associated with the color. The most probable expla- 
nation of the fact that such curves do represent very closely the 
color transformations in certain instances is that K T (see equation 
(23)) is so small that the dissociation brought about by salt for- 
mation leaves (In - ) dominant. 

In other words it is, after all, the degree of dissociation, as 
determined by the hydrogen ion concentration, that determines 
which tautomer predominates. Therefore, consideration of the 
tautomeric equilibria only modifies the original Ostwald treat- 
ment to this extent : the true dissociation constant is a function of 
the several equilibrium and ionization constants involving the 
different tautomers and must be replaced by what Acree calls the 
"total affinity constant," or by what Noyes calls the "apparent 
dissociation constant," when it is desired to show directly how 
the color depends upon the hydrogen ion concentration. 

Many indicators are poly-acidic or poly-basic and will not 
rigidly conform to the treatment for a simple monovalent acid 
such as we have described. Phenolphthalein, for instance, as 
was shown by Acree (1908) and by Wegscheider (1908) must be 



THEORY OF INDICATORS 



61 



considered as poly-acidic. The proper equations to apply 
in this case have been given by Acree (1907, 1908) and also by 
Wegscheider (1908, 1915). According to Acree and his students 
(Acree, 1908) (Acree and Slagle, 1909) the chief color change in 
phenolphthalein is associated with the presence of a quinone 
group and with the ionization of one of the phenol groups. In 
the sulfon phthalein series of indicators Acree and his students 
(White, 1915, and White and Acree, 1918) have found much the 
same sort of condition. 

In the sulfon phthalein series, however, certain unique proper- 
ties described by Lubs and Acree (1916) make the series eminently 
suited for experimental demonstration of the seat of color change. 

In the sulfon phthalein group of indicators we have to deal 
with poly-acids; but as Acree has shown, the dissociation con- 
stant of the strong sulfonic acid group is so very much greater 
than that of the weak phenolic group, with which the principal 
color change is associated, that there is no serious interference. 
As shown in Chapter I we may, therefore, plot the curves for the 
chief color-changes as if we were dealing with monobasic acids. 

The structures of all the sulfon phthaleins are analogous to 
that of phenol sulfon phthalein (phenol red) whose various tau- 
:omers are given by Lubs and Acree (1916) in the following 
scheme : 

C 6 H 4 OH 
I 
: 6 H 4 -C(C 6 H 4 OH) 2 -» C 6 H 4 -C-C 6 H 4 OK -* C 6 H 4 -C(C 6 H 4 OK) 2 
II' II II 

30 2 - O S0 2 - O S0 2 - O 

A colorless B colorless C colorless 



C 6 H 4 OH 

I 
^6H 4 — C : CeEU : O 
I 

30 2 -OH 
) slightly colored 



C 6 H 4 OH 

I 
CeH 4 — C : CeH 4 : 
I 

S0 2 0- + H+ 
E slightly colored 



C 6 H 4 0-K+ 
l I I 
CeH 4 — C : CeH 4 : 



C 6 H 4 OH 

I 
— ► CeH 4 — C '. C6H 4 ! O 
I 

S0 2 0- + K+ 
F slightly colored 

i ■ 

C 6 H 4 0-+K+ 
I 
CeH 4 — C i CeH 4 lO 



S0 2 0" + K+ 
H deeply colored 



S0 2 0- + K+ 
G deeply colored 



62 THE DETERMINATION OF HYDROGEN IONS 

The colorless lactoid A by reason of the strong tendency of 
the sulfonic acid group to ionize goes over into the quinoid struc- 
tures illustrated in the second line which are slightly colored 
yellow. It is the transformation of F to G and H, the ionization 
of the phenolic group forming a quinone-phenolate structure 
which correlates with the intense red color of phenol sulfon 
phthalein (phenol red). 

Just as the discovery of tautomerism seemed at first to discredit 
the original form of the Ostwald theory of color change, so it is 
now realized that a mere change in structure is of itself quite 
inadequate to account for the change in the light absorption upon 
which the color of a solution depends. Light is an electro- 
magnetic phenomenon and the absorption of the energy in any 
particular train of light is undoubtedly due to the resonance of 
electrons. Thus the direct connection between light absorption 
and molecular structure will be found in the relation of molecular 
structure to the distribution and freedom of the component 
electrons. It is in this direction that Baly (1915) believes a 
satisfying theory of the colors of dyes will be found. Although 
Baly has called attention to difficulties in the correlation of colors 
with tautomeric changes there seems to be no inherent reason 
why tautomerism, alteration of the fields of force within the 
molecule, electrolytic ionization and color should not be corre- 
lated. The original Ostwald theory may yet prove to be essen- 
tially correct in that the charging of a molecule by ionization 
should cause a redistribution of the fields of force. Whether or 
not a molecular rearrangement or absorption of a particular train 
of visible light follows may well depend upon particular cir- 
cumstances. But of course all this is left to the future and to 
quantitative data. 

OPTICAL ASPECTS 

While the color changes of indicators are correlated with molec- 
ular rearrangements controlled by hydrogen ion concentrations, 
it should not be forgotten that the phenomena observed are opti- 
cal and tnat no theory of indicators can be considered complete 
enough for practical purposes which fails to recognize this. As 
ordinarily observed in laboratory vessels the color observed 



THEORY OF INDICATORS 63 

is due to a somewhat complex set of phenomena. It is unfortu- 
nate that we have no adequate treatment of the subject which 
at the same time embraces electrolytic dissociation, tautomerism 
and the optical phenomena in a manner directly available in the 
practical application of indicators. The simultaneous treatment 
of these various aspects is necessary before we can feel quite 
sure of our ground when dealing with discrepancies often 
observed in the comparison of colorimetric and electrometric 
measurements of biological fluids. 

Let us first consider the range of an indicator as it is determined 
by the differentiating power of the eye. An approximate treat- 
ment of this is all that will be attempted. 

Using equation (10), cf. page 26: 

1 a 

pH = log — + log 



K (1 - a) 

we find on differentiation that the rate of increase in a with 
increase of pH is: 



da 



d( P H) 
When 



a. 



a (1 — a). 



- 0, a - i< 



d(pH) 2 2 

In other words the maximum rate of increase in dissociation is at 
the half transformation point. This fixes a reference point when 
indicators are to be employed in distinguishing differences in pH. 
The question now arises whether or not this is the central point 
oi the optimal conditions for differentiation of pH values. It 
may be said at once that it is not, because the eye has not only 
to detect differences but also to resolve these differences from the 
3olor already present. Experience shows that the point of maxi- 
mum rate of increase in a is near one limit of the useful range and 
'hat this range lies on the side of lower color. Thus, in 
:he case of the one-color indicator phenolphthalein, the useful 
?one lies between about 8.4 and 9.8 instead of being cen- 
tred at 9.7 which corresponds with the point of half-transforma- 
ion. In the case of a two-color indicator such as phenol red the 



64 THE DETERMINATION OF HYDROGEN IONS 

same reasoning holds, because the eye instinctively fixes upon the 
very dominant red. With other two-color indicators the principle 
holds except when there is no very great difference in the com- 
mand upon the attention by one or the other color. 

It should be mentioned however that these more or less empiri- 
cal relations are observed in comparing virages at equal incre- 
ments of pH when the indicator concentration is adjusted to 
emphasize the differences among the less intensely colored tubes. 
By suitable dilution of the indicator the differences among the 
tubes having the higher percentage color may be emphasized 
and the useful range of the indicator slightly extended. In prac- 
tice this is a procedure which requires care for it is easy to be- 
come confused when dealing with different concentrations of the 
same indicator. 

The fixing of the lower limit of usefulness of a given indicator 
involves another factor. There is the question of the total 
indicator which may be brought into action. A dilute solution 
of phenolphthalein may appear quite colorless at pH 8.4 while 
a much stronger solution will show a distinct color which would 
permit distinguishing 8.2 from 8.4. But the concentration is 
limited by the solubility of the indicator and therefore must be 
taken into consideration. In short there is no basis upon which 
to fix definite limits to the pH range of a given indicator, and 
those limits which are given must be considered to be arbitrary. 
On the other hand the. apparent dissociation curve is quite 
definitive; and were it not for the greater convenience of the 
"range of usefulness" it would be preferable to define the charac- 
teristics of an indicator in terms of its apparent dissociation 
constant. 

We ordinarily speak of color as it if were an entity. As a mat- 
ter of fact the color exhibited by an indicator in solution is due to 
the selective absorption of certain frequencies of the incident 
light. This results in the partial or complete blocking off of the 
light in one or more regions of the spectrum, as may be seen by 
the dark band or bands which appear when the solution is viewed 
through a spectroscope. The transmitted light instead of being 
of the continuous spectrum which blends to subjective white is 
made up of the unaffected wave lengths and of those wave trains 
the intensities of which have been reduced to a greater or lesser 



THEORY OF INDICATORS 65 

extent. The resultant subjective color must be distinguished from 
the color associated with a definite region of the spectrum. 

We come now to the consideration of a phenomenon which is 
undoubtedly exhibited with all indicators but which is generally 
not noticed except in special instances. In some of these instances 
it becomes of great importance and may lead to serious error unless 
recognized. The phenomenon we speak of is the dichromatism 
exhibited, for instance, by solutions of brom phenol blue. Solu- 
tions of this indicator appear blue when viewed in thin layers but 
red in deep layers. The explanation is as follows : The dominant 
absorption band of the alkaline solution is in the yellow and the 
green, so that the transmitted light is composed almost entirely 
of the red and blue. The incident light has an intensity which 
we may call I. After transmission through unit thickness of 
solution some of the light has been absorbed and the intensity 
becomes la, where a is a fraction — the transmission coefficient — 
which depends upon the nature of the absorbing medium and the 
wave length of the light. After traversing thickness e the inten- 
sity becomes Ia e . Now the transmitted blue is Ib«b € and the 
transmitted red I r a r e . We do not happen to know what the 
actual values are, but, merely to illustrate the principle, let us 1 
assume first that the intensity of the incident blue is 100 and of the 
red 30 and that a^ = 0.5 and a t = 0.8. 

For e = 1, Ibab* = 50 and I r a r 6 = 24. Hence blue greater than 
red. 

For' e = 10, Ibflb 6 = 0.01 and I r a r e = 0.30. Hence blue less than 
red. 

This example indicates that the solution may appear blue 
when viewed through thin layers while it may appear red when 
viewed through thick layers. 

If we change the relative intensities of the incident red and blue 
we can change the color of a given thickness of solution. If in 
the above example we reversed the intensities of the incident red 
and blue, then, 

For e = 1, I b flb e = 15 and I r a r € = 80, or red greater than blue. 

This is essentially what happens when we carry the solution 
•rom daylight, rich in blue, to the light of an electric carbon fila- 



66 THE DETERMINATION OF HYDROGEN IONS 

ment lamp, poor in blue. The solution which appears blue in 
daylight appears red in the electric light. 

The practical importance of recognizing the nature of this 
phenomenon may be illustrated in the following way. Suppose 
we have a solution rich in suspended material such as bacterial 
cells, and that we wish to determine its pH value by using brom 
phenol blue. If we view such a solution in deep layers very little 
of the light incident at the bottom reaches the eye. A large 
proportion of the light which does reach the eye is that which 
has entered from the side, has been reflected by the suspended 
particles, and has traversed only a relatively thin section of the 
solution. In such a solution then, if it is of the proper pH, brom 
phenol blue will appear blue, while in a clear comparison solution 
of the same pH the indicator appears red or purple if the tube is 
viewed lengthwise. A comparison is therefore impossible under 
these conditions. If, however, we view the two solutions in rela- 
tively thin layers, as from the side of a test tube, they will appear 
more nearly comparable. There will still remain, however, a 
clearly recognizable difference in the quality of the color which 
serves as a warning that the two solutions are not being compared 
under proper conditions. 

Now a change in the quality of the light in which the turbid 
and the clear solutions are compared will, of course, not avert 
one fundamental difficulty — a difference in effective path; but a 
proper change in the quality of the light can eliminate the di- 
chromatism and free the eye from one source of confusion. In 
the case at hand we might eliminate either the red or the blue. 
Which had best be eliminated is a question which can not be 
answered properly until we have before us the necessary spectro- 
metric measurements. Nevertheless the following observations 
made with a small hand spectroscope, and the deductions there- 
from may prove to be illuminating. 

i The chief absorption bands of brom phenol blue solutions occur 
in the yellow-green range and in the blue. In alkaline solutions 
the band in the blue disappears while that in the yellow widens 
into the green. As the solution is made more acid the band in 
the blue appears, shutting off the transmitted blue, while that in 
the yellow-green contracts, permitting the passage of the green. 
Our light source then should be such that at least one of these 



THEORY OF INDICATORS 67 

changes may become apparent, and at the same time either the 
blue or red must be eliminated. The light of the mercury arc 
fulfills these conditions. It is relatively poor in red and it emits 
yellow, green and blue fines where the shifts in the absorption 
bands of brom phenol blue occur. Since the mercury arc is not 
generally available we have devised a light source to fulfill the 
alternative condition, namely, one which will permit observation 
of the contrasts due to the shift in the yellow-green band 1 and 
which at the same time is free from blue. Such a source is found 
in electric light from which the blue is screened by a translucent 
paper painted with a yellow, acid solution of phenol red. One dis- 
advantage of such a screen is that the red transmitted through 
it is so dominant that it obscures the contrasts which are due 
to the shifting of the yellow-green absorption band. Nevertheless, 
such a screen has proved useful in pH determinations with brom 
phenol blue and particularly useful with brom cresol purple. 
In either case it is most useful in the more acid ranges covered 
by these indicators. 

The device consists of an ordinary box of convenient size in 
which are mounted three or four large electric lights (e.g., 30 cp. 
3arbon filaments). A piece of "tin" serves as reflector. The box 
nay be fined with asbestos board. A piece of glass, cut to fit the 
Dox, is held in place on one side by the asbestos lining and on the 
)ther by a few tacks. This glass serves only to protect the screen 
md is not essential. The screen is made from translucent paper 
mown to draughtsmen as "Economy" tracing paper. It is 
stretched across the open side of the box and painted with a 
solution consisting of 5 cc. of 0.6 per cent phenol red and 5 cc. 
)f M/5 KH 2 P0 4 (stock, standard phosphate solution) . While the 
)aper is wet it is stretched and pinned to the box with thumb 
acks. This arrangement may be constructed in a very short 
ime and will be found very helpful in many cases. It should be 
ised in a dark room or, if such a room is not available, exterior 
ight may be shut off with a photographer's black cloth. 

While considering light sources we may call attention to the 
: act that all the sulfon phthalein indicators may be used in elec- 

1 This should not be confused with the changes in "subjective color." 
~_ n the screened light no participation of transmitted green will be detected 
1 y the unaided eye. 



68 THE DETERMINATION OF HYDROGEN IONS 

trie light, although brom thymol blue and thymol blue are not 
well adapted for use in light poor in blue. Doubtless a more 
thorough investigation of the absorption spectra of the sulfon 
phthalein indicators will make it possible to devise light sources 
which will materially increase their efficiency. 

So far as we have been able to detect with instruments at hand, 
the absorption spectra of all the indicators of the sulfon phthalein 
series are such that the appearance of dichromatism must be 
expected under certain conditions. It will be observed with phe- 
nol red in light relatively poor in red and rich in blue, for example, 
the light of a mercury arc; and with thymol blue in light relatively 
poor in blue and rich in red for example, ordinary electric light. 

When the colorimeter is employed in the study of colored solu- 
tions the applicability of Beer's law is assumed. This may be 

Lii O2 

expressed in the form, — = — where Ci and C 2 represent the 

concentrations of color in two solutions and Li and L 2 represent 
the depths of solution traveled by the light when a color match 
occurs. Applying this relation one is able to obtain the ratio of 
concentrations and therefrom the concentration in one solution 
if the concentration in the other be known. But as was shown 
above we have, in the case of two-color indicators, different trans- 
mission coefficients for various regions of the spectrum. Conse- 
quently the depth of a solution cannot be altered as it is in the 
ordinary colorimeter without seriously affecting the quality of the 
emergent light. 

When such shifts in quality occur it is impossible without the 
aid of elaborate photometric devices to make an accurate com- 
parison of intensities. This at once limits the usefulness of the 
ordinary colorimeter, a cardinal principle of which is an accurate 
device for varying and measuring the depth of view. That 
feature of certain instruments whereby two optical fields are 
brought into juxtaposition remains most useful. 

This last and other mechanical features should at once be de- 
veloped for the colorimeter devised by Gillespie (1921) which 
promises to be of very great value in exact indicator work. The 
principle of Gillespie's colorimeter is shown in figure 10. The 
vessels A, B, C, D and E are of colorless glass the bottoms of 
which should be optically polished plane-parallel. A and C are 



THEORY OF INDICATORS 



69 



fixed while B may be moved up or down. The position of B is 
indicated on a scale the zero mark of which corresponds to the 
position of B when B and C are in contact and the 100 mark 
of which corresponds to the position of B when B is in contact 
with A. If now there is placed in B a solution of the acid form 
of an indicator and in C a solution of the same concentration of 
the indicator transformed completely to the alkaline form, it is 
obvious that the position of the vessel B will determine the ratio 
of the two forms of the indicator which will be within the view. 



*i A 

B 
C 








D 










E 





Fig. 10. Diagrammatic Section op Gillespie's Colorimeter 

For comparison studies a solution to be tested is placed in E 
together with that concentration of indicator that occurs in the 
optical system B-C. For colored solutions tubes A and D are 
used as in the Walpole system, which will presently be described. 
As Gillespie has indicated this colorimeter should be useful for 
certain general work where the exact principles of colorimetry 
have often been neglected. 

There have been two chief methods of dealing with the interfer- 
ing effect of the natural color of solutions. The first method, 
used by S0rensen, consists in coloring the standard comparison 
solutions until their color matches that of the solution to be tested, 
md subsequently adding to each the indicator. 



70 THE DETERMINATION OP HYDROGEN IONS 

S0rensen's coloring solutions are the following : 

a. Bismarck brown (0.2 gram in 1 litre of water). 

b. Helianthin II (0.1 gram in 800 cc. alcohol, 200 cc. water). 

c. Tropeolin O (0.2 gram in 1 litre of water). 

d. Tropeolin OO (0.2 gram in 1 litre of water). 

e. Curcumein (0.2 gram in 600 cc. alcohol, 400 cc. water). 
/. Methyl violet (0.02 gram in 1 litre of water) . 

g. Cotton blue (0.1 gram in 1 litre of water). 

The second method was introduced by Walpole (1910). It con- 
sists in superimposing a tube of the colored solution over the 
standard comparison solution to which the indicator is added, 
and comparing this combination with the tested solution plus 
indicator superimposed upon a tube of clear water. 

A somewhat crude but nevertheless helpful application of Wal- 
pole's principle may be made from a block of wood. Six deep 
holes just large enough to hold ordinary test tubes are bored 
parallel to one another in pairs. Adjacent pairs are placed as 
close to one another as can be done without breaking through the 
intervening walls. Perpendicular to these holes and running 
through each pair are bored smaller holes through which the test 
tubes may be viewed. The center pair of test tubes holds first 
the solution to be tested plus the indicator and second a water 
blank. At either side are placed the standards colored with the 
indicator and each backed by a sample of the solution under test. 
This is the so called "comparator" of Hurwitz, Meyer, and 
Ostenberg (1915). Before use it is well to paint the whole block 
and especially the holes a non-reflecting black. To produce a 
"dead" black use a soft wood and an alcohol wood-stain. This 
simple comparator is illustrated in figure 7. 

One or another of the means described serves fairly well in over- 
coming the confusing influence of moderate color in solutions to 
be tested. In bacteriological work, however, a most serious diffi- 
culty is presented by the suspension of cells and precipitates. 

If one views lengthwise a tube containing suspended particles, 
or even particles of grosser colloid dimensions, much of the light 
incident at the bottom is absorbed or reflected before it reaches 
the eye, and, if the tube is not screened, some of the light which 
reaches the eye is that which has entered from the side and has 
been scattered. Consequently, a comparison with a clear standard 
is inadequate. 



THEORY OF INDICATORS 71 

S0rensen (1909) has attempted to correct for this effect by the 
use of a finely divided precipitate suspended in the comparison 
solution. This he accomplishes by forming a precipitate of 
BaS0 4 through the addition of chemically equivalent quantities 
of BaCl2 and Na 2 S0 4 . Strictly speaking, this gives an imperfect 
imitation, but like the attempt to match color it does very well 
in many instances. The Walpole superposition method may be 
used with turbid solutions as well as with colored, as experience 
with the device of Hurwitz, Meyer and Ostenberg has shown. In 
passing, attention should be called to the fact that the view of a 
turbid solution should be made through a relatively thin layer. 
When the comparison is made in test tubes, for instance, the view 
should be from the side. 

There are some solutions, however, which are so dark or turbid 
that they cannot be handled with much precision by any of these 
methods. On the other' hand a combination of these methods 
with moderate and judicious dilution [as was indicated in Chap- 
ter II this may not seriously alter the pH of a solution], permits 
very good estimates with solutions which at first may appear 
impossible. Some of the deepest colored solutions permit reason- 
ably good determinations "and when sufficiently transparent per- 
mit the application of spectrometric devices. Turbidity on the 
other hand is sometimes unmanageable. Even in the case of 
milk where comparison with a standard is out of the question a 
two colored indicator presents a basis for judgment. 

This brings us to a phase of the question the detailed analysis 
of which will not be attempted. It may simply be stated as a 
fact of experience that the color change of a two-color indicator, 
presenting as it does change in intensities of what we may sum- 
marily describe as two colors, is a change in quality which is 
unmistakable within narrow limits. When there is added to this 
that brilliancy which is characteristic of the sulfon phthalein 
indicators the subjective aspect of indicator work is taken care 
of in a way that may surprise one. 

The spectrophotometer and allied instruments which have 
served in many of the investigations of indicators have not yet 
been brought within the range of ordinary colorimetric procedure 
for the determination of pH. Where there occurs a great change 
in the absorption bands, as at the endpoint of a titration, the hand 



72 THE DETERMINATION OF HYDROGEN IONS 

spectroscope may be applied but it is doubtful if such an instru- 
ment is of much value for slight differences of virage. For the 
possibilities which remain for development in this field the reader 
is referred to the special literature. 

This brief sketch of some of the principal aspects of indicator 
theory would be incomplete were attention not called to the value 
of indicators for demonstrating to students important relations 
among acids and bases. Indicators also call our attention to 
molecular transformations which we seldom think of as occurring 
among substances the light absorptions of which are in regions of 
the spectrum beyond the reach of the eye. 

And finally, indicator colors bring to the thoughtful observer 
their own intrinsic beauty and also reminders of how far we have 
come along the road of understanding and of how very, very far 
we still have to go. 



CHAPTER V 
Choice of Indicators 

From the enormous number of colored compounds found in 
nature and among the products of the laboratory many have 
been called into use as acidimetric-alkalimetric indicators. Among 
those of plant origin litmus and alizarine are the more familiar. 
One indicator of animal origin, cochineal, an extract of an insect, 
was formerly used to some extent. Walpole's (1913) treatment 
of litmus, Walbum's (1913) study of the coloring matter of the 
red cabbage and some of the more recent work, has given us a 
little data on properties of plant and animal pigments which are 
applicable to hydrogen ion determinations. But for the most 
part indicators of natural origin have been neglected for the study 
of synthetic compounds. 

Litmus has played so important a role in acidimetry that it is 
worthy of brief, special mention. 

Litmus is obtained by the oxidation in the presence of ammonia 
of the orcin contained in lichens, generally of the species Roccella 
and Lecanora. The material which comes upon the market is 
frequently in the form of cubes composed of gypsum or similar 
material and comparatively little of the coloring matter. The 
coloring matter is a complex from which there have been isolated 
many compounds, chief among which are azolitmin, erythrolitmin, 
erythrolein and spaniolitmin. Of these the azolitmin is the most 
important; but the azolitmin of commerce is of uncertain compo- 
sition, Scheitz (1910). The composition of the different prepara- 
tions varies with the source and also with the extent of the action 
of alkali and air upon the crude material. 

The following method of preparing a sensitive litmus solution 
is taken from Morse (1905). 

The crushed commercial litmus is repeatedly extracted with fresh quan- 
tities of 85 per cent alcohol for the purpose of removing a violet coloring 
matter which is colored by acids but not made blue by alkalies. The resi- 
due, consisting mainly of calcium carbonate, carbonates of the alkalies and 
the material to be isolated, is washed with more hot alcohol upon a filter 

73 



74 THE DETERMINATION OF HYDROGEN IONS 

and then digested for several hours with cold distilled water. The filtered 
aqueous extract has a pure blue color and contains an excess of alkali, a 
part of which is in the form of carbonate and a part in combination with 
litmus. To remove the alkaline reaction the solution is heated to the boil- 
ing point and cautiously treated with very dilute sulfuric acid until it be- 
comes very distinctly and permanently red. Boil till all CO2 is dispelled. 
Treat with a dilute solution of barium hydroxide until the color changes to 
a violet. Filter, evaporate to a small volume and precipitate the litmus 
with strong alcohol. Wash with alcohol and dry. 

Dr. P. Rupp (private communication) prefers to make a final 
washing with water which removes much of the salt at the expense 
of some dye. 

Synthetic indicators have for the most part displaced those of 
natural origin until litmus and alizarine, turmeric and cochineal 
are becoming more and more unfamiliar in the chemical labora- 
tory. Indeed Bjerrum (1914) states that the two synthetic indi- 
cators, methyl red and phenolphthalein, particularly because of 
the zones of hydrogen ion concentration within which they change 
color, are sufficient for most titrimetric purposes. 

But the two indicators mentioned above cover but a very lim- 
ited range of hydrogen ion concentration so that they are insuf- 
ficient for the purpose we now have under consideration. A sur- 
vey of indicators suitable for hydrogen ion determinations was 
opened in Nernst's laboratory in 1904 by Salessky. This survey 
was extended in the same year by Friedenthal, by Fels and by 
Salm and the results were summarized in Salm's famous table 
(cf. Z. physik. Chem., 57). 

Then came the classic work of S0rensen of the Carlsberg lab- 
oratory in Copenhagen. The array of available indicators had 
become so large as to be burdensome. S0rensen in an extensive 
investigation of the correspondence between colorimetric and 
electrometric determinations of hydrogen ion concentrations re- 
vealed discrepancies which were attributed mainly to the influence 
of protein and salts. He chose those indicators which were rela- 
tively free from the so-called protein and salt errors, constructed 
solutions of known and reproducible hydrogen ion concentra- 
tions and thus furnished the biochemist with selected tools of beau- 
tiful simplicity. It is well to emphasize the labor of elimination 
which S0rensen performed because without it we might still be 
consulting such tables as that published by Thiel (1911), or the 



CHOICE OF INDICATORS 75 

ponderous tables 8-19, pages 84-94, and be bewildered by the 
very extensive array. 

S0rensen's work, coupled as it was with a most important con- 
tribution to enzyme chemistry gave great impetus to the use of 
indicators in biochemistry. His selection of indicators was there- 
fore soon enlarged by additions of new indicators which fulfilled 
the criteria of reliability which he had laid down. Alpha naphthol 
phthalein, a compound first synthesized by Grabowski (1871), 
was shown by S0rensen and Palitzsch (1910) to have a range 
of pH 7-9 and was found useful in biological fluids. Methyl red 
(Rupp and Loose, 1908) was given its very useful place by the 
investigations of Palitzsch (1911). Henderson and Forbes (1910) 
introduced 2-5 di nitro hydroquinone as an indicator possessing 
several steps of color change and therefore useful over a wide range 
of pH. Walpole (1914) called attention to several indicators of 
potential value. Hottinger (1914) recommended "lacmosol," 
a constituent of lacmoid, and Scatchard and Bogert (1916) 
advocated the use of dinitro benzoylene urea. There remain a 
host of indicators which have been tried out in the empirical 
practices of titration but which have never had their pH ranges 
determined ; and there remain an unlimited number of possibilities 
embodied in existing compounds such as Dox's (1915) phenol 
quinolinein, Rupp's (1915) syntheses in the methyl red series 
and untouched homologues of phenol phthalein and of phenol 
sulfon phthalein. Furthermore, there undoubtedly are still 
unsynthesized compounds of various types, old and new, which 
will some day displace those now in use. 

In 1915 Levy, Rowhtree and Marriott, without applying the 
tests of reliability which S0rensen had employed, used phenol 
sulphon phthalein in determining the pH of the dialyzate of blood. 
This compound, first synthesized in Remsen's laboratory by Sohon 
(1898), has received considerable attention from Acree and his 
co-workers because it furnishes excellent material for the quinone- 
phenolate theory of indicators. To further such studies Acree 
and White had synthesized new derivatives of phenol sulphon 
phthalein at the time when the work of Levy, Rowntree and 
Marriott attracted the attention of Clark and Lubs. These authors 
. were looking for more brilliant indicators for use in bacterial cul- 
ture media and were attracted by the well known brilliance of 



76 THE DETERMINATION OF HYDROGEN IONS 

phenol sulphon phthalein. Through the courtesy of Professor 
Acree some of the derivatives which White had prepared were 
obtained. New homologues were synthesized by Lubs. The 
applicability of these and numerous other indicators in the deter- 
mination of the pH values of biological fluids was then studied. 

In the sulfon phthalein series the following were studied: 

Phenol sulfon phthalein, Sohon (1898). 

Tetra nitro phenol sulfon phthalein, White and Acree (1915). 

Phenol nitro sulfon phthalein, Lubs and Clark (1915). 

Tetra bromo phenol sulfon phthalein, White and Acree (1915). 

Tetra chloro phenol sulfon phthalein, Lubs and Clark. 

Ortho cresol sulfon phthalein, Sohon (1898). 

Di bromo ortho cresol sulfon phthalein, Sohon (1898). 

Thymol sulfon phthalein, Lubs and Clark (1915). 

Thymol nitro sulfon phthalein, Lubs and Clark. 

Di bromo thymol sulfon phthalein, Lubs and Clark (1915). 

a-napthol sulfon phthalein, Lubs and Clark (1915). 

Carvacrol sulfon phthalein, Lubs and Clark. 

Orcinol sulfon phthalein, Gilpin (1894). 

The attractiveness of methyl red led to the study of the fol- 
lowing compounds : 

o-carboxy benzene azo mono methyl aniline, Sive and Jones 
(1915). 

o-carboxy benzene azo di methyl aniline, Rupp and Loose 
(1908). 

o-carboxy benzene azo mono ethyl aniline, Lubs and Clark 
(1915). 

o-carboxy benzene azo di ethyl aniline, Lubs and Clark (1915). 

o-carboxy benzene azo mono propyl aniline, Lubs and Clark 
(1915). 

o-carboxy benzene azo di propyl aniline, Lubs and Clark (1915). 

o-carboxy benzene azo (?) amyl aniline, Lubs and Clark (1915). 

o-carboxy benzene azo di methyl a naphthyl amine, Howard 
and Pope (1911). 

o-carboxy benzene azo a naphthyl amine, Howard and Pope 
(1911). 

o-carboxy benzene azo di phenyl amine, Howard and Pope 
(1911). 

Meta carboxy benzene azo di methyl aniline, Lubs and Clark. 



CHOICE OF INDICATORS 77 

The mono alkyl homologues of methyl red were found to be 
much less brilliant than the di alkyl compounds and were there- 
fore rejected. For the same reason or because of large protein 
errors we rejected the other compounds with the exception of 
di ethyl and di propyl red. Of these we retained di propyl red 
because it is very useful in solutions of a little lower hydrogen ion 
concentration than those which may be studied with methyl red. 

Propyl red is, however, not included in table 6 because it 
precipitates too easily from buffer solutions to be of general 
usefulness. 

As the result of an extensive series of comparisons between 
colorimetric and electrometric measurements, made for the most 
part upon solutions of interest to bacteriologists, Clark and Lubs 
(1917) suggested the series of indicators given in table 6. This 
series is made up for the most part of the brilliant and more 
reliable sulfon phthaleins but contains the still indispensable but 
not very stable methyl red. 

In the course of their investigations these authors resurrected 
ortho cresol phthalein (Baeyer and Freude, 1880), found it quite 
as reliable as phenolphthalein and more brilliant with a color 
better adapted to titrations in artificial light. 

In spite of the fact that S0rensen rejected the greater number 
of the indicators which he studied and that Clark and Lubs, after 
a resurvey of the subject and the preparation of many new com- 
pounds, listed but few indicators as reliable, there has recently 
appeared a tendency to resurrect the rejects. Now many of 
these are useful in special cases and undoubtedly there is an 
occasional individual to be found in the lists which has been 
insufficiently studied and unjustly rejected. Nevertheless, the 
indiscriminate use of miscellaneous indicators may lead to gross 
errors or at least to such a diversity of data that their correlation 
will become complex during the coming period when the Specific 
salt-errors and general conduct of the individual indicators are 
still being worked up. 

It is therefore advisable to use the more thoroughly studied 
lists. Three such lists are given (tables 5, 6 and 7). The indi- 
cators therein listed should cover all ordinary needs. S0rensen's 
list is given in table 5 and to this is appended S0rensen's 
comments. For general purposes the selection of indicators given 



78 



THE DETERMINATION OF HYDROGEN IONS 



in table 6 will be found the most satisfactory especially because 
of their brilliancy. Each of these however has its own special 
limitations as every indicator has. For the study of colorless 
solutions where salt errors are to be reduced the nitro phenols 
listed in table 7 should be valuable. 

TABLE 5 

Sfirenseri's selected indicators 

Figures in parentheses refer to Schultz (1914). Figures 1-20 are S0rensen's 



INDICATOR 



10. 
11. 

12. 
18. 

14. 
15. 
16. 
17. 

18. 
10. 

20. 



Methyl violet 6B extra, (517) 

Mauvein, Rosolane, (688) 

Diphenylamino-azo-benzene 

Diphenylamino-azo-p-benzene sulfonic acid, Tro- 
paeolin 00, (139) 

Diphenylamino-azo-m-benzene sulfonic acid, Metanil 
yellow, (134) 

Benzyl anilino-azo-benzene 

Benzylanilino-azo-p-benzene sulfonic acid 

Metachloro diethyl-anilino-azo-p-benzene sulfonic 
acid 

Dimethyl anilino-azo-benzene, (32) 

Methyl orange, Helianthine, (138) 

a naphthylamino-azo-benzene 

a-naphthylamino-azo-p-benzene sulfonic acid 

Para nitro phenol 

Neutral red, (670) 

Rosolic acid, Aurin, (555) 

Orange I, Tropaeolin 000 No. 1, (144) 

Phenolphthalein. 

Thymolphthalein 

Paranitrobenzene-azo-salicylic acid, Alizarine yel- 
low R, (58) 

Resorcin-azo-p-benzene sulfonic acid, Tropaeolin 0, 
(143) 



pH RANGE 


0.1- 


3.2 


0.1- 


2.9 


1.2- 


2.1 


1.4- 


2.6 


1.2- 


2.3 


2.3- 


3.3 


1.9- 3.3 


2.6- 


4.0 


2.9- 4.0 


3.1- 


4.4 


3.7- 


5.0 


3.5- 


5.7 


5.0- 7.0 


6.8- 


8.0 


6.8- 


8.0 


7.6- 8.9 


8.3- 


10.0 


9.3- 


10.5 


10.1- 


12.1 


11.1- 


12.7 



In tables 8-20 are a few indicators which are undoubtedly 
reliable but little used, a few which are definitely unreliable 
though often used, and very many of uncertain character but 
for the most part bearing the stamp of disapproval by competent 
judges. Since the indicators in tables 5, 6 and 7 cover all ordinary 
requirements it seems hardly worth while to venture upon an 
analysis of the remaining tables. 



CHOICE OF INDICATORS 79 

In table 5 is S^rensen's list of indicators; concerning these indicators 
S0rensen remarks: 

Not all these indicators furnish equally well defined virages and above 
all they are not of equal applicability under all circumstances. In the 
choice of an indicator from among those which we have been led to recom- 
mend it is necessary to use judicious care and especially to take into con- 
sideration the following facts: 

a. The indicators of the methyl violet group (nos. 1 and 2) (see table 5) 
are especially sensitive to the action of neutral salts; furthermore the in- 
tensity of color changes on standing and the change is the more rapid the 
more acid the medium. 

b. The basic indicators (nos. 3, 6, 9, 11, 14) are soluble in toluene and in 
chloroform. The first four separate partially on prolonged standing of 
the experimental solution. 

c. In the presence of high percentages of natural proteins most of the in- 
dicators are useless although certain of them are still serviceable; nos. 1, 2, 
13, 16, 17, 18. 

d. In the presence of protein decomposition products even in consid- 
erable proportions the entire series of indicators may render real service. 
Yet even in these conditions some of the acid azo indicators may give 
notable errors (nos. 4, 5, 7, 8, 10) in which case one should resort to the cor- 
responding basic indicators. 

e. When only small percentages of protein or their decomposition prod- 
ucts are concerned the acid azo indicators are more often preferable to 
the basic for they are not influenced by toluene or chloroform and do not 
separate from solution on standing. 

/. In all doubtful cases — for example in. the colorimetric measurement 
of solutions whose manner of reaction with the indicator is not known, the 
electrometric measurement as a standard method should be used. Then 
the worth of the indicator will be determined by electrometric measurement 
with colorimetric comparison. 

In table 6 will be found the final selection of Clark and Lubs 
with the common names which they suggested for laboratory par- 
lance, the concentration of indicator convenient for use, a rough 
indication of the nature of the color, and the useful pH range. 

With the improved method for the preparation of the sulfon 
phthalein indicators described by Lubs and Clark (1915) they may 
easily be made from materials readily obtained. The indicators 
can also now be purchased in this country and abroad from 
chemical supply houses. 

The indicators recommended by Clark and Lubs are marketed 
both in the form of a dry powder and in stock solutions. In cases 
where the acidity of the free acid dye in the indicator solution 



80 



THE DETERMINATION OF HYDROGEN IONS 



does not interfere with accuracy and when alcohol is not objec- 
tionable the alcoholic solutions of the dyes may be used. Clark 
and Lubs prefer to use aqueous solutions of the alkali salts in 
concentrations which may be conveniently kept as stock solu- 
tions. These are diluted for the test solutions used in the drop- 
ping bottles. 

TABLE 6 
Clark and Lubs' list of indicators 



CHEMICAL NAME 


COMMON NAME 


S5 
I 

B < 
o 


COLOR CHANGE 


RANGE 

PH 


Thymol sulfon 
phthalein (acid 
range) 


Thymol blue (see 
below) 

Brom phenol blue 

Methyl red 

Brom cresol pur- 
ple 

Brom thymol blue 

Phenol red 

Cresol red 

Thymol blue 

Cresol phthalein 


per cent 

0.04 

0.04 

0.02 

0.04 

0.04 
0.02 
0.02 
0.04 
0.02 


Red-yellow 

Yellow-blue 

Red-yellow 

Yellow-purple 

Yellow-blue 

Yellow-red 

Yellow-red 

Yellow-blue 

Colorless-red 


1.2-2.8 


Tetra bromo phenol 
sulfon phthalein 

Ortho carboxy ben- 
zene azo di methyl 
aniline 


3.0-4.6 
4.4-6.0 


Di bromo ortho cre- 
sol sulfon phthal- 
ein 


5.2-6.8 


Di bromo thymol 
sulfon phthalein 

Phenol sulfon phthal- 
ein 


6.0-7.6 
6.8-8.4 


Ortho cresol sulfon 
phthalein 


7.2-8.8 


Thymol sulfon 
phthalein 


8.0-9.6 


Ortho cresol phthal- 
ein 


8.2-9*8 







For the preparation of these stock solutions one decigram (0.1 
gram) of the dry powder is ground in an agate mortar with the 
following quantities of N/20 NaOH. When solution is complete 
dilute to 25 cc. with water. 



CHOICE OF INDICATORS 



81 



MOLECULAR WEIGHT 


INDICATOR 


N/20 NaOH per 

DECIGRAM 


354 
669 
382 
540 
466 
624 
269 


Phenol red 
Brom phenol blue 
Cresol red 
Brom cresol purple 
Thymol blue 
Brom thymol blue 
Methyl red 


CC. 

5.7 
3.0 
5.3 
3.7 
4.3 
3.2 
7.4 



If there be no particular reason to maintain exact equivalents 
it may be found easier to dissolve the dyes in 1.1 equivalents of 
alkali instead of one -equivalent as indicated above. 

When made up to 25 cc. as noted above there is obtained in 
each case a 0.4 per cent solution of the original dye itself. For 
tests they should be diluted further. To place the dyes upon a 
comparable basis the final dilution should be nearly the same when 
calculated upon a molar basis and, by reason of the great change in 
molecular weight caused by the introduction of bromine and other 
group substituents, equal molecular concentrations will be very 
far apart in percentage concentration. For all ordinary pur- 
poses, however, this may be neglected and the solutions mentioned 
above if diluted in each case to a concentration of 0.04 per 
cent will be found satisfactory for use in testing 10 cc. of a solu- 
tion with about five drops of indicator. 

From various sources have come complaints that the method 
outlined above for the preparation of the aqueous alkali salt 
solution of brom cresol purple leads to a solution of much lower 
tinctorial power than when the same material is taken up directly 
in alcohol. No such difficulty was experienced with the material 
described by Lubs and Clark but it has appeared not infrequently 
since. The source of the difficulty is not yet definitely traced, 
but is suspected to be due to impurities. If so it should be 
avoided by purchasing the highly purified material which is now 
made specially. 

While the aqueous alkali salt solution of methyl red is preferred 
for some purposes a methyl red solution can be more conveniently 
prepared by dissolving 1 decigram in 100 cc. alcohol and diluting 
to 200 with distilled water. 



82 THE DETERMINATION OF HYDROGEN IONS 

Ortho cresol phthalein and phenol phthalein are used in a 
0.04 per cent solution of 95 per cent alcohol. 

Methyl red and brom cresol purple may be recrystallized from 
hot toluol, cresol red and brom phenol blue from glacial acetic 
acid, thymol blue from hot alcohol. 

Tables 8-20 have been compiled with the aid of Dr. Barnett 
Cohen and Dr. Elias Elvove with several purposes in view. In 
the first place there exist in the older literature a great many 
observations recorded in terms of the color of a given indicator. 
These data can often be translated into modern terms if the pH 
range of the given indicator is known. In the second place there 

TABLE 7 

Michaelis' indicators and their ranges as used in the method of Michaelis and 

Gyemant (see Chapter VIII) 

Picric acid colorless 0.0- 1.3 yellow 

2, 4-dinitro phenol colorless 2.0- 4.7 yellow 

a dinitro phenol 

2, 6-dinitro phenol colorless 1.7- 4.4 yellow 

/3 dinitro phenol 

2, 5-dinitro phenol colorless 4.0- 6.0 yellow 

y-dinitro phenol 

m-nitro phenol colorless 6.3- 9.0 yellow 

p-nitro phenol colorless 4.7- 7.9 yellow 

Phenolphthalein colorless 8.5-10.5 red 

Alizarine yellow GG colorless 10.0-12.0 yellow 

Salicyl yellow 

are circumstances when for one reason or another it becomes 
necessary to draw upon the miscellaneous list. It should there- 
fore be available. Lastly, and perhaps most important, our review 
of the literature and of indicator labeling has shown that there 
is great confusion and an initial step in the clarification of the 
subject will be taken if there is available a tabulation of existing 
data to serve as a basis for revision. 

In examining a large collection of indicators the labeling 
was found to be insufficient in a large percentage of cases. On 
studying the literature we find evidence that others have 
encountered the same difficulty without stating so, for in 
many instances the indicator names given were evidently those 



CHOICE OF INDICATORS 83 

of one or another dealer who cared so little for the scientific uses 
of his commodity that he left from the label the designation 
essential to its identification. This habit has become more or less 
prevalent. In some instances our own uncertainty may be due 
to an arbitrary adherence to the nomenclature found in various 
editions of Schultz. For instance when we see the indicator 
crocei'ne listed and refer to Schultz (1914) we find four crocei'nes 
with various distinguishing marks and seven other compounds 
for the names of which "croceme" is used in one or another com- 
bination. But Schultz lists no croceme. We are not helped in going 
back to the lists of Schultz and Julius (1902). Now we might 
assume that "croceme" was used in Salm's table as a term having 
a definite meaning outside the dye industry. On this principle 
we should find that "helianthine" has been employed in accordance 
with scientific usage. However we find that an old sample of 
helianthine from Salm's dealer is not the helianthine of methyl 
orange but corresponds in pH-range to Salm's Helianthine I, 
which, together with Salm's Helianthine II we have not identified. 

Again there are other difficulties such as are illustrated by the 
case of Tropaeolin OOO No. 1 and Tropaeolin 000 No. 2. No. 1 
is prepared from p-sulfanilic acid and a-naphthol. No 2 is pre- 
pared from p-sulfanilic acid and (3-naphthol. In this there is 
agreement by Schultz and Julius 1902, Green 1904 and Beilstein 
(third edition). In accord with this S0rensen describes his 
a-naphthol preparation as Tropaeolin 000 No. 1. In the second 
edition of Indicators and Test Papers, Cohn (1914) has given 
synonyms for the a and /3 compounds which agree with Green, 
but has reversed the No. 1 and No. 2 at the headings of his de- 
scriptions and uses "No. 1" and "No. 2" inconsistently in the 
text. Prideaux (1917) has called the /3 compound Tropaeolin 
000 and gives the range as 7.6-8.9, which looks suspiciously like 
S0rensen's 7.6-8.9 for the a compound. Prideaux uses the 
synonym. Orange II for the /3 compound in .harmony with Green 
but on the next page describes the a compound as Orange II. 
The identity of Salm's Tropaeolin 000 is not clear. It was 
evidently different from the Tropaeolin 000 No. 1 used by 
S0rensen. We find that an old sample with the label "Tro- 
paeolin 000" agrees with neither S0rensen's nor Salm's data. 

Many other instances might be cited to show the confused 



84 



THE DETERMINATION OF HYDROGEN IONS 



state of the subject. Because it is serious the reader will have 
to use the following tables with caution, and he need not be 
surprised if a sample of indicator which he tests does not give 
a pH range corresponding to that recorded. 

In the compilation of the lists we have followed competent 
advice in using the nomenclature of Farbstofftabellen, Gustav 

TABLE 8 
Nitro compounds 



SERIAL 
NUM- 
BER 


INDICATOR 


pH RANGE 


1 


Picric acid (5) 


colorless 

colorless 
light yellow 

colorless 

colorless 

colorless 

pink 

colorless 
colorless 
colorless 
colorless 

colorless 
pink 


0.0- 1.3 yellow 

1.7- 4.4 yellow 
2.0- 4.0 yellow 

2.0- 4.7 yellow 
3.0- 9.0 various 
colors 
3.9- 5.9 yellow 

4.0- 6.0 yellow 

4.1— 5.6 yellow 


2 
3 


2, 4, 6-trinitro-phenol 

2, 6-Dinitro-phenol (fi) 

Martius yellow (6) 


4 
5 

6 

7 
8 


2, 4-dinitro-a-naphthol 

2, 4-Dinitro-phenol (a) 

2, 5-Dinitro-hydroquinone 

2, 3-Dinitro-phenol (e) 

2, 5-Dinitro-phenol (7) 

iso-Picramic acid 


9 
10 


2, 6-dinitro-4-amino- 
phenol 

3, 4-Dinitro-phenol (5) 

p-Nitro-phenol 


4.3- 6.3 yellow 
5.0- 7.0 yellow 


11 
12 


Dinitrobenzoylene-urea .. . . 

m-Nitro-phenol 


6.0- 8.0 yellow 
6.3- 9.0 yellow 


13 


Nitramine (?) 


11.0-12.5 


14 
15 


1, 3, 5-Trinitro-benzene 

2, 4, 6-Trinitro-toluene (TNT) 


11.5-14.0 orange 
11.5-14.0 orange 



Schultz, fifth revised edition, Berlin, 1914. In a few cases there 
have been added to the synonyms in table 20 terms which are 
obsolete in the dye industry but which are still used in the nomen- 
clature of indicators. Schultz numbers are to be found in tables 8 
to 19 following the name of each indicator when the given indi- 
cator is listed by Schultz. Since it is unimportant for indicator 
work, no distinction has been made between acids and their salts. 
The classification by structure follows in the main that of Schultz. 



CHOICE OF INDICATORS 



85 



TABLE 9 
Monoazo compounds 



SERIAL 








NUM- 


INDICATOR 




pH RANGE 


,BER 








16 


Curcumein (?) 


orange 


0.0- 1.0 yellow, 








yellow 13- 








15 green 


17 


o-Carboxybenzene-azo-(di or 








mono?) amyl-aniline . . . 


purple 


0.0- 1.6 orange (fluo- 
rescent), 
orange 5.6- 
7.6 yellow 


18 


o-Carboxybenzene-azo-m- 










yellow 


0.0- 4.6 orange, 

orange 4.6- 
7.6 yellow 


19 


p-Toluene-az o-pheny 1-aniline . 




1.0- 2.0 


20 


p-Carboxybenzene-azo-di- 
methyl-aniline (Para 








methyl red) 


red 


1.0- 3.0 yellow 


21 


p-Toluene-azo-pbenyl-a-naph- 








thylamine 




1.1- 1.9 


22 


Benzene-azo-diphenylamine. . 




1.2- 2.1 


23 


Metanil yellow extra (134).... 
m-sulfobenzene-azo-di- 
phenylamine 


red 


1.2-2.3 yellow 


24 


Benzene-az o-pheny 1-a-n aph- 








thylamine 




1.4- 2.6 


25 


Orange IV (139) 


pink 


1.4- 2.6 yellow 




p-sulfobenzene-azo-di- 








phenylamine 






26 


o-Toluene-azo-o-toluidine. . . . 




1.4- 2.9 


27 


p-Toluene-azo-benzyl-a- 








naphthylamine 




1.6- 2.6 


• 28 


p-Toluene-azo-benzyl-aniline. 




1.6- 2.8 


29 


Benzene-azo-benzyl-a-naph- 












1.9- 2.9 


30 




light yellow 


1.9- 3.3 yellow 


31 


p-Benzenesulfonic acid-azo- 








aniline 




1.9- 3.3 


32 


p-Benzenesulfonic acid-azo- 






benzyl-aniline 




1.9- 3.3 


33 


m-Carboxybenzene-azo-di- 








methylaniline 


red 


2.0- 4.0 yellow 
2.3- 3.3 


34 


Benzene-azo-benzyl-aniline.. . 





86 



THE DETERMINATION 
TABLE 9- 



OF HYDROGEN IONS 

Continued 



SERIAL 








NUM- 


INDICATOR 




pH RANGE 


BER 








35 


p-Benzenesulfonic acid-azo- 
metachloro-dimethyl- 








aniline 




2.6- 4.0 


36 


Orange III (47) 


red 


2.6- 4.6 yellow 




m-nitrobenzene-azo-/3- 






naphthol-3, 6-disulfo- 








nic acid 






37 


Butter yellow (32) 


red 


2.9- 4.0 yellow 




benzene-azo-dimethyl- 






aniline 






38 


o-Carboxybenzene-azo-di- 








phenylamine 


pink 


3.0- 4.6 yellow, 

purple 0.0- 












1.6 pink 


39 


p-Benzenesulfonic acid-azo- 








methyl-aniline 




3.1- 4.2 


40 


p-Benzenesulfonic acid-azo- 








ethyl-aniline 




3.1- 4.4 


41 


Methyl orange (138) 


orange red 


3.1- 4.4 yellow 




p-benzenesulfonic acid- 




az o-dimethy 1-aniline 






42 


p-Benzenesulfonic acid-azo- 
diethyl-aniline (Ethyl 








orange) 


pink 


3.5- 4.5 yellow 


43 


p-Benzenesulfonic acid-azo- 




a-naphthylamine 




3.5- 5.7 


44 


Benzene-azo-a-naphthyl- 








amine 




3.7- 5.0 


45 


p-Toluene-azo-a-naph- 






thylamine 




3.7- 5.0 


46 


o-Carboxybenzene-azo-mono- 








methylaniline 


red 


4.0- 6.0 yellow 


47 


Chrysoidin (33) 


orange 


4.0- 7.0 yellow 




benzene-azo-m-phenyl- 




enediamine 






48 


o-Carboxybenzene-azo-mono- 








ethylaniline 


red 


4.2- 6.2 yellow 


49 


o-Carboxybenzene-azo-mono- 






n-propylaniline 


red 


4.2- 6.2 yellow 


50 


o-Carboxybenzene-azo-di- 

methylaniline (Methyl 








red) 


red 


4.2- 6.3 yellow 


51 


o-Carboxybenzene-azo-di- 








ethvlaniline 


red 


4.4- 6.2 yellow 






' J v 



CHOICE OF INDICATORS 
TABLE 9— Concluded 



87 



1ERIAL 






NUM- 


INDICATOR 


pH RANGE 


BER 






52 


o-Carboxybenzene-azo-di-n- 
propylaniline (Propyl 






red) 


red 4.6- 6.6 yellow 


53 


Benzene-azo-dimethyl-a- 






naphthylamine 


4.8- 5.5 


54 


p-Benzenesulfonic acid-azo- 
dimethyl-a-naph- 






thylamine 


5.0- 5.7 


55 


o-Carboxybenzene-azo-a- 






naphthylamine 


pink 5.6- 7.0 yellow 


56 


o-Carboxybenzene-azo-di- 
methyl-a-naphthyl- 






amine 


red 5.6- 7.6 orange 


57 


Naphthylamine brown (160) . . 
4-sulf onaphthalene-az o- 
a-naphthol 


orange 6.0- 8.4 pink 


58 


6-Sulf o-a-naphthol-1-az o-m- 






hydroxybenzoic acid . . . 


orange 7.0- 8.0 blue, 

violet 12- 
13 red 


59 


Orange I (144) 


7.6- 8.9 




p-sulfobenzene-azo-a- 






naphthol 




60 


Orange II (145) 


7.6- 8.9 (?) 




p-sulfobenzene-azo-/S- 






naphthol 




61 


Alizarine yellow GG (48) 
m-nitrobenzene-azo-sali- 
cylic acid 


colorless 10.0-12.0 yellow 


62 


Alizarine yellow R (58) 

p-nitrobenzene-azo-sali- 
cylic acid 


pale yellow 10.1-12.1 orange . 


63 


Fast red A (161) 


10.5-12.1 




5-sulfonaphthalene-azo- 






/3-naphthol 




64 


Fast red B (112) 


pink 10.5-12.5 orange 




a-naphthalene-azo-/8- 






naphthol-3, 6-disulfo- 






nic acid 




55 


Chrysoin (143) 

p-sulfobenzene-azo- 
resorcin 


yellow 11.1-12.7 orange 


36 


Orange G (38) 


yellow 11.5-14.0 pink 




benzene-azo-/8-naphthol- 




7-disulfonic acid 





88 



THE DETERMINATION OF HYDROGEN IONS 



TABLE 10 
Disazo compounds 



SERIAL 






NUM- 


INDICATOR 


pH RANGE 


BER 






67 


Benzopurpurin B (365) 


blue-0.3- 1.0 violet, 




ditolyl-disazo-bi-/3-naph- 


violet 1.0- 




thylamine-/3-sulfonic 


5.0 yellow, 




acid 


yellow 12.0- 
14.0 rose 


68 


Congo (307) 


blue 3.0- 5.0 red 




diphenyl-disazo-binaph- 






thionic acid 




69 


Azo blue (377) 


violet 10.5-11.5 pink 




ditoly 1-disaz o-bi-a-n aph- 






thol-4-sulfonic acid 





TABLE 11 
Triphenylmethane compounds 



SERIAL 








NUM- 


INDICATOR 




pH RANGE 


BER 








70 


Crystal violet (516) 


green 


0.0- 2.0 blue 




hexamethyl pararo- 






saniline 






71 


Malachite green (495) 


yellow 


0.0- 2.0 green, 




tetramethyl-di-p-amino- 




blue 11.5- 




triphenyl-carbinol 




14.0 fades 


72 


Red violet 5R extra (514) 

mixture of mono-, di- and 
tri-methyl or ethyl ro- 
sanilines and pararo- 
sanilines 


green 


0.0- 2.0 blue 


73 


Brilliant green (499) 


yellow 


0.0- 2.6 green 




tetraethyl-di-p-amino- 








triphenyl-carbinol 






74 


Iodine green 


yellow 


0.0- 2.6 blue 




heptamethyl rosaniline 




75 


Ethyl violet (518) 


yellow 


0.0- 3.6 blue 




hexaethyl pararosaniline 






76 


Ethyl green (methyl green)... 
ethyl-hexamethyl-para- 
rosaniline bromid 




0.1- 2.3 





CHOICE OF INDICATORS 89 




TABLE 11- 


■Continued 


tERIAL 
NUM- 
BER 

77 

78 
79 
80 

81 
82 


INDICATOR 


pH RANGE 


Methyl violet 6B extra (517).. 
mixture of benzyl-tetra- 
and pentamethyl-p- 
rosaniline and hexa- 
methyl-p-rosaniline 

Fuchsin (512) (base) 


0.1- 3.2 

purple 1.2- 3.0 fades 
pink 3.6- 6.0 colorless 


mixture of rosaniline and 
pararosaniline 
Red violet 5ES (525) 


trisulfonate of ethyl ro- 
saniline 
Water blue (539) 


blue 4.7- 7.0 colorless,* 


di- and tri-sulfonic acids 

of triphenyl-p-rosani- 

line and di-phenyl-ro- 

saniline 

Aurin (p-rosolic acid) (555)... 

complex mixture 
Alkali blue (536) 


purple 10.5- 
14.0 rose 

yellow 6.9- 8.0 red 
lilac 9.4-14.0 pink 


83 


mixture of diphenyl-ro- 
saniline-mono-sulfonic 
acid and triphenyl- 
pararosaniline-mono- 
sulfonic acid 
Methyl blue (538) 


blue 10.0-13.0 pink 


84 


triphenylpararosaniline- 
di- and trisulf onic acids 
Fuchsin S (524) 


red 12.0-14.0 fades 




di- and trisulfonic acids 
of rosaniline and p-ro- 
saniline 





* Samples of Water blue (China blue) which we have tested vary con- 
si lerably. The color change in the neutral range is instantaneous with 
s< me samples but requires a long period (several hours at room tempera- 
t\ re) for others. 

TABLE 12 
Quinoline compounds 



81 RIAL 
1 OTH- 
ER 


INDICATOR 


pH RANGE 


55 


Quinoline blue (Cyanin) (611). 
C28H35N2I 


colorless 7.0-8.0 violet 



TABLE 18 
Oxazine compounds 



SERIAL 






NUM- 


INDICATOR 


pH RANGE 


BER 






86 


Alizarin green B (657) 


lilac-0.3- 1.0 flesh, 




dihydroxy-naphth-azox- 


brownish yel- 




onium sulfonate 


low 12.0- 
14.0 brown, 
then green 


87 


Nile blue 2B (654) 


blue 7.2- 8.6 rose 




diethyl-benzyl-diamino- 






naphtho-phenazoxon- 






ium chlorid 




88 


Nile blue A (653) 


blue 10.2-13.0 rose 




diethyl-diamino-naphtho- 






phenazoxonium sulfate 





TABLE 14 

Azines 



SERIAL 








NUM- 


INDICATOR 




pH RANGE 


BER 








89 


Methylene violet BN powder 








(680) 


purple 


0.0- 1.2 violet 




dimethyl-diamino- 








phenyl-phenaz onium 








chloride 






90 


Rosolane (688) 




0.1- 2.9 




phenyl and tolyl 








safranines 






91 


Rose magdala (694) 


rose 


3.0- 4.0 red, 




mixtures of amino naph- 




lilac 12.0- 




thyl-naphthazonium 




14.0 violet 




chlorid and diamino- 








n aphthy 1-n aphthaz on- 








ium chloride 






92 


Indulin, spirit soluble (697) . . 
mixtures of dianilido- 
amido-tri-anilido- and 
tetranilido-phenyl- 
phenazonium chlorides 


blue 


5.6- 7.0 violet 


93 


Neutral red (670) 


red 


6.8- 8.0 yellow 




dimethyl-diamino-tolu- 








phenazine 






94 


Neutral blue (676) 




9.3-10.2 




dimethyl-amino-phenyl- 








phenonaphthazonium 








chloride 







90 



CHOICE OF INDICATORS 



91 



TABLE 15 
Anthraquinone compounds 



iERIAL 










NUM- 


INDICATOR 




pH RANGI 




BER 










95 


Alizarin Blue X (803) 

dihydroxy-anthra- 
quinone-/S-quinoline 


pink 


0.0-1.6 


yellow, 
yellow 6.0- 
7.6 green 


96 


Purpurin (783) 


yellow 


0.0-4.0 


orange, 




1, 2, 4-trihydroxy-anthra- 






orange 4.0- 




qumone 






8.0 rose, 
lilac 12.0- 
14.0 violet 


97 


Alizarin red S (780) 


yellow 


5.0-6.8 


pink 




mono sulfonic acid of 








alizarin Vi 








98 


Alizarin Vi (Alizarine) (778)... 
1, 2-dihydroxy-anthra- 
quinone 


yellow 


5.5-6.8 


red, 

violet 10.1- 
12.1 purple 


99 


Alizarin Blue S (804) 


yellow 


6.0-8.0 


green, 




Na bisulfite compound of 




green 11.0- 




alizarin blue X 






13.0 blue 



TABLE 16 
Indigos 



E 3RIAL 
DUM- 
BER 



.00 



INDICATOR 



Indigotine la in powder (In- 
digo carmine) (877) . . . 
Indigo disulfonate 



pH RANGE 



blue 11.6-14.0 yellow 



92 



THE DETERMINATION OF HYDROGEN IONS 



TABLE 17 
Phthalein and xanthone compounds 



SERIAL 

NUM- 
BER 


INDICATOR 


pH RANGE 


101 


Rhodamine B (573) 


orange - 
yellow 

orange 

orange 

pink 

light yellow 

yellow 

yellowish 
yellowish 
colorless 
colorless 
colorless 
colorless 
colorless 
pink 


-0.1- 1.2 pink 
0.0- 2.6 brown, 


102 


diethyl m-amino-phenol- 
phthalein 
Gallein (599) 


103 


pyrogallol phthalein 
E©sin G (587) 


brown 3.6- 
7.0 pink, 

pink 9.4- 
14.0 purple 
0.0- 3.0 pink 

0.0- 3.6 pink 

1.4- 3.6 red 

3.6- 5.6 yellow (fluo- 
rescent) 

4.0- 6.6 yellow (fluo- 
rescent) 

7.0- 9.0 green 

7.0- 9.0 blue 

8.0- 9.0 violet 

8.2- 9.8 red 


104 


tetrabromo fluorescein 
Erythrosin* 


105 
106 

107 


Phloxin Red BH (Griibler). . . 
Uranin (Fluorescein) (585) . . . 

resorcin phthalein 
Dichloro fluorescein 


108 
109 
110 
111 


o-a-Naphthol phthalein 

p-a-Naphthol phthalein 

Tetrabromophenol phthalein. 
o-Cresol phthalein 


112 


Phenol phthalein 


8.3-10.0 red 


113 

114 


1, 2, 3-Xylenol phthalein 

Thymol phthalein 


8.9-10.2 blue 
9.3-10.5 blue 


115 


Eosin BN (590) 


10.5-14.0 yellow 




dibromo dinitro fluo- 
rescein 



* The identity of this erythrosin is in doubt. Erythrosin R, G, yellow- 
ish, and Iodeosin G are synonyms of di-iodo-fluorescein. Erythrosin extra 
bluish, D, B, J extra, JNV, W extra, and Iodeosin B are synonyms for the 
tetra-iodo-fluorescein . 



CHOICE OF INDICATORS 



93 



TABLE 18 
Sulfonphthaleins 



SERIAL 








NUM- 


INDICATOR 




pH RANGE 


BER 








116 


Di-iodophenol sulfon- 








phthalein* 


orange 


0.0- 1.2 yellow, 








yellow 3.2- 






/ 


7.0 purple 


117 




pink 


0.2- 0.8 orange, 

yellow 4.0- 

7.0 green, 
violet 8.5- 

10.2 blue, 
blue 10.2- 

12.5 green 


118 


Thymol sulf onphthalein 
Thymol blue 








(acid range) 


red 


1.2- 2.8 yellowf, 




(alkaline range) 




yellow 8.0- 


119 


Tetranitrophenol sulfon- 




9.6 blue 




phthalein 


yellow 


2.8- 3.8 red 


120 


Tetrabromophenol sulfon- 






phthalein 


yellow 


3.0- 4.6 blue 




Brom phenol blue 






121 


Tetrachlorophenol sulf on- 








phthalein 


• yellow 


3.0- 4.6 blue 


122 


Dibromo-o-cresol sulfon- 






phthalein 


yellow 


5.2- 6.8 purple 




Brom cresol purple 






.23 


Dibromothymol sulfon- 








phthalein 


yellow 


6.0- 7.6 blue 




Brom thymol blue 






24 


Phenol nitro sulf onphthalein. 


yellow 


6.6- 8.4 purple 


25 


Phenol sulf onphthalein 

Phenol Red 


yellow 


6.8- 8.4 red 


26 


o-Cresol sulfonphthalein 

Cresol Red 


yellow 


7.2- 8.8 red 


27 


Salicyl sulfonphthalein 


yellow 


7.2- 9.2 pink 


28 


Thymol nitro sulfonphthalein. 


yellow 


7.2- 9.4 blue 


29 


a-Naphthol sulfonphthalein . . 


yellow 


7.5- 9.0 blue 


30 


Carvacrol sulfonphthalein 


yellow 


7.8- 9.6 blue 


31 


Orcin sulfonphthalein 


yellow 


8.6-10.0 pink (fluo- 
rescent) 


32 


Nitrothymol sulfonphthalein. 


violet 


9.2-11.5 yellow 



* Purity not established. 

f All sulfonphthaleins show color changes at high acidities but those 
o thymol sulfonphthalein are the most useful. 



TABLE 19 
Miscellaneous indicators 



SERIAL 








NUM- 


INDICATOR 




pH RANGE 


BER 








133 


Croceine (?) 


■ blue - 


-0.3- 0.0 rose, 








rose 12.0- 








14.0 violet 


134 




green 


-0.3- 1.0 blue, 

violet 14.0- 
15.0 lilac 


135 


Safranin (679?) 


blue- 


-0.3- 1.0 red, 

red 14.0- 
15.0 violet 


136 


Hematein (Logwood) (938) . . . 


variable 








from 


0.0-15.0 


137 


Gentian violet 




0.4- 2.7 


138' 


Red cabbage extract 


red 


2.4- 4.5 green 


139 


1-Oxy-naphtho-chino- 






methane 


colorless 


2.7- 3.7 purple 

2.8- 4.0 yellow 


140 


Troger and Hille's indicator. . 


orange 




C 14 H 16 N4SOsH 


< 




141 


Phenacetolin 


yellow 


3.0- 6.0 red, 






red 10.0- 








13.0 colorless 


142 


Lacmosol 


red 
red 
red 


4.4— 5.5 blue 


143 


Lacmoid 


4.4- 6.2 blue 


144 


Azolitmin (Litmus) 


4.5- 8.3 blue 


145 


Carminic acid (from cochi- 








neal) (932) '. 


orange 


4.6- 7.8 rose, 






violet 11.0- 








14.0 pink 


146 


Cochineal (932) 


yellow 
pink 


4.8- 6.2 lilac 


147 


Archil (Orchil) (934) 


5.6- 7.6 lilac 


148 


Brazil wood, Redwood, Bra- 






silein (935) 


colorless 


6.0- 8.0 pink 
7.0- 8.0 greenish 
7.3- 8.7 green 


149 


Guaiac tincture 


colorless 


150 


Lygosine 


yellow 




di-o-hydroxy-styryl 




ketone 






151 


Mimosa flower extract 




7.7- 9.6 


152 


Turmeric (Curcuma) (927) . . . 
C21H20O6 


yellow 


8.0-10.2 orange 


153 


Alkanin 


red 
yellow 
purple 
orange 


8.3-10.0 blue 


154 


a-Naphthol benzein 


8.5- 9.8 green 


155 


Benzoazurin (?) 


10.5-12.0 pink 
11.0-12.0 orange red 


156 


Helianthin I (?) 


157 


Poirrier's blue 


blue 
brownish- 
yellow 


11.0-13 red 


158 


Helianthin II (?) 








13.0-14.0 lilac 



94 



CHOICE OF INDICATORS 



95 



TABLE 20 
The more common synonyms of indicators 

This table contains the names and synonyms of the various indicators 
in alphabetical order. Following each name, or group of synonyms, is a 
number in bold face type. This number is the serial number of the com- 
pound as found in the preceding tables. 

Some names apply to two or more entirely different dyes. If such dyes 
are in our tables, their serial numbers are given; and if the particular dyes 
are not in the preceding tables there is given in italics in parentheses the 
1914 Schultz number and name. Thus: "Helianthin, 36, 41 (141, Azogelb 
SG cone.)," means that the name Helianthin is applied to Orange III, to 
Methyl orange and to Schultz No. 141, Azogelb 3G cone. 



Acetin blue R 92 

Acid fuchsin, B, G, O, S 84 

Acid magenta, 84 

Acid orange 60 

Acid yellow, cryst, D extra, DMP 25 

Acid yellow RS 65 

Acme yellow 65 

Alizarin, le 98 

Alizarin-Blaustich I and la 98 

Alizarin blue A, ABI, BM in Teig, C, 
DNW in Teig, F, G, GG, GW, R, 
RR, RR in Teig, WA in Teig, WC, 
WN in Teig, WR, WRR, WX, X, XA 

in Teig 95 

Alizarin blue S, SR, SRW, SW 99 

Alizarin blue soluble ABS 99 

Alizarin carmine 97 

Alizarin dark blue S, SW 99 

Alizarin green B 86 

Alizarin mono sulfonate 97 

Alizarin No. 1 98 

Uizarin No. 6 96 

Uizarin orange R, 2R-paste and powder.. 62 

Uizarin P 98 

Uizarin powder SA, W, W extra 97 

dizarin purpurin 96 

dizarin red IWS, S 97 

. dizarin sulfacid 97 

. dizarin yellow G, GG, GGW, 3G paste 

and powder 61 

. dizarin yellow R, RW paste and powder 62 

. lizarin VI 98 

. lizarin violet 102 

L lkah" blue, B-5B, No. 2, No. 4, No. 6, 

R-5R, RR 82 

i lkanin , 153 

i midoazobenzol 30 

i nilin brown 78 

i nilin purple 90 

i nilin red 78 

i nilin yellow 3, 30 

i nthracene yellow GG 61 



Anthracene yellow RN 62 

Anthracene violet 102 

Anthraquinone compounds Table 15 

Archelline 2B ." . . . 64 

Archil 147 

Atlas orange 60 

Aurin 81 

Azalein 78 

Azin blue spirit soluble 92 

Azines Table 14 

Azo blue 69 

Azo-bordeaux 64 

Azolitmin 144 

Azo compounds Table 9 

Baumwollrot 4B 68 

(.363, Benzopurpurin 4B) 

Baumwollrot B 67, 68 

Baumwollrot C 68 

Beizengelb2 GT 61 

Beizengelb 3R, PN 62 

Benzal green 00 71 

Benzoazurin 155 

Benzoin blue R 69 

Benzopurpurin B 67 

Benzyl violet, 7B 77 

Betanaphthol orange 60 

Bitter almond oil green 71 

Blau CB, spirit sol 92 

Bleu alcalin, 4B 82 

Bleu 3BS, C4B, de Lyon 80 

Bleu methyl 83 

Bleu neutre 94 

Bleu Nicholson 4B ' 82 

Bleu soluble pur 80 

Blue extra, water soluble for wool and 

silk 80 

Bogert and Scatchard's indicator 11 

Bordeaux B, BL, R, R extra 64 

Bordeaux G 64 

(254, Bordeaux G) 

Brasilein; brasilin 148 

Braun salz R 47 



96 



THE DETERMINATION OF HYDROGEN IONS 



TABLE 20- Continued 



Brazil wood 148 

Brilliant f uchsin 78 

Brilliant green, crystals, cryst. No. 1, 3, 

4, extra, II, O, S, Y 73 

Brilliant violet 6B, 8B 77 

Brom cresol purple 122 

Brom eosin 103 

Brom phenol blue 120 

Brom thymol blue 123 

Butter yellow 37 

Campeche wood 136 

Cardinal, R, G 78 

Cardinal red 63 

Cardinal red B, G, R 78 

Carmine, lake 146 

Carminic acid 145 

Cerasin 63 

Cerasine, R ' 64 

China blue 80 

China green cryst 71 

Chrombrown RO 57 

Chrysoidin 47 

(84, Chrysoidin R) 
Chrysoidin A cryst., -Fettfarbe, G, 2G 

extra, J, JEE, RE, Y, Y extra 47 

Chrysoidin R 47 

(34 also 69, Chrysoidin R) 

Chrysoin, G 65 

Citronine V double 25 

Cochineal 146 

Congo; Congo red; Congo red R 68 

Corallin 81 

Cotton blue 80, 83 

Cotton blue 3B, cone. No. 1, No. 2, cone. 

R, extra 80 

Cotton red B 67, 68 

Cotton red, cone 68 

Cresol red 126 

Croceine 133 

Crystal violet, extra cryst. 5B, 5BO, 6B, 

N powder, O, P cryst 70 

Cudbear 147 

Curcuma 152 

Curcumein* 16 

Curcumin 152 

Cyanin 85 

Dahlia 72 

Dechan's indicator 102 

Degener's indicator 141 

Diamant f uchsin 78 

Diamant griin 71 

Diamant grttn B 71 

(276, Diamantgrun B) 

Diamant grttn G 73 

Dianilrot R 68 

Disazo compounds Table 10 

Dianthine B 104 



Dichlorofluorescein 107 

Dimethylaniline orange 41 

Diphenylamin blue 83 

Direct red C 68 

Ecarlate J, JJ, V 115 

Echtblau B spirit sol., R spirit sol 92 

EchtbraunN 57 

Echtgrttn 71 

(1, SolidgrUn O in Teig) 

Echtrot A, AV, 63 

Echtrot B, P extra 64 

Emerald green cryst 71 

Eosine bleuatre, bluish 104 

Eosin, B extra, DH, extra water sol., G, 
G extra, GGF, 2G, I yellowish, J 
extra, JJF, 3J, 4J extra, KS ord., MP, 
OO extra, S extra yellowish, yellowish, 

Y extra 103 

Eosin B, BN, BW, DHV, I blfiulich, S 

extra bluish 115 

Eosin J 104 

Eosin methylene blue 134 

Eosin scarlet, B, BB extra 115 

Erythrosin B, bluish, extra bluish, D, 

J extra, JNV, W extra 104 

Ethyl green 73, 76 

Ethyl orange 42 

Ethyl red 51 

Ethyl purple 6B 75 

Ethyl violet 75 

Fast brown N 57 

Fast pink for silk 91 

Fast red A 63 

Fast red B, P extra 64 

Fast red cone 63 

Fluorescein 106 

Formanck's indicator 86 

Fuchsia 89 

Fuchsin acid 84 

Fuchsin base 78 

Fuchsin, 6B, crystals, FCOO, la cryst., 

NB, NG, RFN, VI cryst., XL 78 

Fuchsin S, SIII, SN, SS, ST 84 

Fustic 72, 84 

Galleln, paste A, SW, W paste and powder 102 

Gentian violet 137 

Gold orange 60 

Gold orange MP 41 

Gold yellow 3, 65 

Green crystals 71 

Guernsey blue 80 

Guaiac tincture 149 

Hematein; Hematoxylin 136 

Helianthin 36, 41 

(141, Azogelb SG cone.) 

Helianthin 1 156 

Helianthin II 158 



* The term curcumein has been applied to several different compounds. 



CHOICE OF INDICATORS 



97 



TABLE 20— Continued 



Helvetia blue 83 

Henderson and Forbes' indicator 5 

Hof mann's violet 72 

Indigen D, F 92 

Indigo carmine, carmine D paste, disul- 

fonate, extract 100 

Indigos Table 16 

Indigotine la powder 100 

Indophenin extra 92 

Indulin base, 2B, BA, opal, spirit soluble, 

RA 92 

Iodeosin B 104 

Iodine green 74 

Jaune beurre 37 

Jaune chrome R 61 

Jaune d'aniline 30 

Jaune d'or 3 

Jaune II 65 

Jaune M, mfitanile extra 230 23 

Jaune naphtol 3 

(7, Naphtolgelb S) 

Iodeosin B 104 

Todviolett 72 

Kaiserrot 115 

Kosmosrot extra 68 

Kristallorange GG 66 

jacmosol 142 

'-.acmoid 143 

jacmus 144 

.lichtblau G 80 

.light green N 71 

.litmus 144 

.ogwood 136 

juck's indicator 113 

iUnge's indicator 41 

: ,yddit 1 

. ivgosine 150 

] fagdala red 91 

1 [agenta 78 

] [alachite green, A cryst., B, cryst. extra, 
cryst. 3, cryst. 4, powder superfine B, 

4B 71 

I Calachite green G 73 

1 "anchester yellow. 3 

1 landarin G 60 

1 !arine blue V 80 

I artius yellow 3 

I auvein 90 

J elinite 1 

J ellet's indicator 58 

J etachrome orange R 62 

J etanil yellow, extra, GR extra cone, 

O, PL 23 

I ethyl blue, for cotton, MBJ, MLB 83 

J ethylene violet BN powder, RRA, 

RRN, 3RA extra 89 

J ethyl eosin B extra 115 



Methyl green 76 

Methyl orange, MP 41 

Methyl red 50 

Methyl violet 5B, 6B, 6B extra, 7B, 10B. . 77 

Methyl water blue 83 

Mimosa extract , 151 

Miscellaneous indicators Table 19 

Naphthalene red, rose 91 

Naphthalene yellow 3 

a-naphthol benzein 154 

a-naphthol orange 59 

Naphthol orange 59 

Naphthol yellow 3 

(7, Naphtolgelb S) 

Naphthylamin brown 57 

Naphthylamin pink 91 

Naphthylamin yellow 3 

Natural indicators Table 19 

Neutral blue 94 

Neutral red, extra 93 

New green, cryst., BI, BII, Bill, GI, 

Gil, GUI 71 

New Victoria green I, II, 71 

New yellow extra 25 

Nicholson's blue 82 

Nierenstein's indicator 139 

Nile blue A, B, R 88 

Nile blue 2B 87 

Nitramine (?) 13 

Nitro compounds, Nitro-phenols Table 8 

NopalinG 115 

Oil yellow 37 

(36, Sudan I) 

Opal blue bluish 80 

Orange A 60 

Orange B 59 

Orange extra 60 

Orange G 60, 66 

(36, Sudan I) 

Orange GG, GG in cryst., GMP 66 

Orange GS, IV 25 

Orange 1 59 

Orange II, IIB, IIP, IIPL 60 

Orange III 36, 41 

Orange MN, MNO 23 

Orange N 25 

(79, Brillantorange R) 

Orange No. 1 59 

Orange No. 2 60 

Orange No. 3 36, 41 

Orange No. 4 25 

Orange P 60 

Orange R 62 

(39, Ponceau G; 151, Orange T) 

Orange R extra 59, 60 

Orange S 59 

Orangd au chrome 62 



98 



THE DETERMINATION OP HYDROGEN IONS 



TABLE 20— Concluded 



Orcein; Orchil 147 

Orcellin No. 4 63 

Orseille, carmine, extract 147 

Oxazine compounds Table 13 

Para methyl red 20 

Paris violet 6B, 7B 77 

Patent orange 66 

Perkin's violet 90 

Phenacetolin 141 

Phenol red 125 

Phenolphthaleins Table 17 

Phenolsulfonphthaleins Table 18 

Phloxin red BH 105 

Phthaleins Table 17 

i-picramic acid 8 

Picric acid 1 

Poirrier's blue 157 

Poirrier's orange II 60 

Pourpre francaise 147 

Primerose soluble 104 

Primula R water sol 72 

Propyl red 52 

Purpurin ' 96 

Pyrosin B '. 104 

Quinoline blue 85 

Quinoline compounds Table 12 

Red cabbage 138 

Red violet, 5R extra 72 

Red violet 5RS 79 

Redwood 148 

Resorcin yellow 65 

Rhodamine B, B extra, 101 

Roccellin 63 

Rosanilin base 78 

Rose B a l'eau 104 

Rosein 78 

Rose magdala 91 

Rosolane 90 

Rosolic acid 81 

Rouge B 64 

Rouge 1 63 

Rouge congo '. 68 

Rouge coton G, direct C 68 

Rouge neutre extra 93 

Rubidin 63 

Rubin 78 

Safranin 135 

Safranin extra bluish 89 

Safrosin 115 



Saure gelb cryst., D extra, DMP 25 

Saure orange. 60 

Silk blue, BTSL 80 

Smaragdgrun cryst 73 

Solid blue base, B spirit sol., RR 92 

Solid green J, JJO 73 

Solid green 4B, cryst. A No. 1, cryst. O, 

cryst. OO, extra J, O, OOJ, P 71 

Soluble blue 80 

(687, Methylblau fur Seide MLB) 

Spirit induline, B, R cone 92 

Spirit yellow, G 30 

Sudan red 91 

Sulfonphthaleins Table 18 

Terra cotta R 62 

Tymol blue 118 

Tournesol 144 

Triphenylme thane dyes Table 1 1 

Troger and Hille's indicator 140 

Tropaeolin G 23, 59 

Tropaeolin O 65 

Tropaeolin OO 25 

Tropaeolin OOO No. 1 59 

Tropaeolin OOO No. 2 60 

Tropaeolin R 65 

Turmeric 152 

Uranin 106 

Vert brillant 73' 

Vert diamond P extra 71 

Vert ethyle extra 73 

Vert J3E, solide B extra, LB extra, solide 

cristaux 71 

Victoria yellow O double cone 23 

Violet 5B, 6B, 7B 77 

Violet 7B extra 70 

Violet au bichromate 90 

Violet benzyle 77 

Violet C, G 70 

Violet Hofmann 72 

Violet meHhyl 6B, 6B extra cone 77 

Violet pate 90 

Violett R, RR, 4RN 72 

Von M tiller's indicator 25 

Walkorange R 62 

Water blue, B, BJJ, R 80 

Wool blue 83 

Xanthone compounds Table 17 

Yellow corallin 81 



CHAPTER VI 
Standard Buffer Solutions for Colorimetric Comparison 

The standard solutions used in the colorimetric method of 
determining hydrogen ion concentrations are buffer solutions with 
such well defined compositions that they can be accurately repro- 
duced, and with pH values accurately defined by hydrogen elec- 
trode measurements. They generally consist of mixtures of some 
acid and its alkali salt. Several such mixtures have been care- 
fully studied. An excellent set has been described by S.^rensen 
(1912). This set may be supplemented by the acetic acid — 
sodium acetate mixtures, most careful measurements of which 
have been made by Walpole (1914), and by Palitzsch's (1915) 
excellent boric acid-borax mixtures. 

Clark and Lubs (1916) have designed a set of standards which 
they believe are somewhat more conveniently prepared than 
are the S0rensen standards. Their set is composed of the follow- 
ing mixtures: 

Potassium chlorid + HC1 
Acid potassium phthalate + HC1 
Acid potassium phthalate + NaOH 
Acid potassium phosphate + NaOH 
Boric acid, KC1 + NaOH 

For a discussion of these mixtures, the methods used in deter- 
mining their pH values, and the potential measurements we refer 
ihe reader to the original paper {Journal of Biological Chemistry, 
1916, 25, no. 3, p. 479). We may proceed at once to describe the 
letails of preparation. 

The various mixtures are made up from the following stock solu- 
tions: M/5 potassium chlorid (KC1), M/5 acid potassium phos- 
)hate (KH 2 P0 4 ), M/5 acid potassium phthalate (KHC 8 H 4 4 ), 
Vl/5 boric acid with M/5 potassium chlorid (H3BO3, KC1), M/5 
odium hydroxid (NaOH), and M/5 hydrochloric acid (HC1). 
Uthough the subsequent mixtures are diluted to M/20 the above 
oncentrations of the stock solutions are convenient for several 
easons. 

99 






100 THE DETERMINATION OF HYDROGEN IONS 

The water used in the crystallization of the salts and in the 
preparation of the stock solutions and mixtures should be redis- 
tilled. So-called "conductivity water," which is distilled first 
from acid chromate solution and again from barium hydroxid, is 
recommended, but it is not necessary. 

M/5 potassium chlorid solution. (This solution will not be 
necessary except in the preparation of the most acid series of 
mixtures.) The salt should be recrystallized three or four times 
and dried in an oven at about 120°C. for two days. The fifth 
molecular solution contains 14.912 grams in 1 liter. 

M/5 acid potassium phthalate solution. Acid potassium phtha- 
late may be prepared by the method of Dodge (1915) modified 
as follows. Make up a concentrated potassium hydroxid solu- 
tion by dissolving about 60 grams of a high-grade sample in 
about 400 cc. of water. To this add 50 grams of the commer- 
cial resublimed anhydrid of ortho phthalic acid. Test a cool por- 
tion of the solution with phenol phthalein. If the solution is still 
alkaline, add more phthalic anhydrid; if acid, add more KOH. 
When roughly adjusted to a slight pink with phenol phthalein 1 
add as much more phthalic anhydrid as the solution contains and 
heat till all is dissolved. Filter while hot, and allow the crystal- 
lization to take place slowly. The crystals should be drained 
with suction and recrystallized at least twice from distilled water. 2 

Crystallization should not be allowed to take place below 
20°C, for Dodge (1920) states: 

A saturated solution of the acid phthalate on chilling will deposit 
crystals of a more acid salt, having the formula 2KHC 8 H 4 04-C8Hg0 4 . 
These crystals are in the form of prismatic needles, easily distinguished 
under the microscope from the 6-sided orthorhombic plates of the salt 
KHCH4O4. 

Dry the salt at 110°-115°C. to constant weight. 

A fifth molecular solution contains 40.836 grams of the salt in 
1 liter of the solution. 

M/5 acid potassium phosphate solution. A high-grade com- 
mercial sample of the salt is recrystallized at least three times 

1 Use a diluted portion for the final test. 

2 Samples of phthalic anhydrid which are now found on the market are 
frequently grossly impure. With some samples ten recrystallizations 
are necessary. Hence it is economy to purchase only the highest grades. 



STANDARD BUFFER SOLUTIONS 101 

from distilled water and dried to constant weight at 110°-115°C. 
A fifth molecular solution should contain in 1 liter 27.232 grams. 
The solution should be distinctly red with methyl red and dis- 
tinctly blue with brom phenol blue. 

M/5 boric acid, M/5 potassium chlorid. Boric acid should be 
recrystallized several times from distilled water. It should be 
air dried 3 in thin layers betweeri filter paper and the constancy 
of weight established by drying small samples in thin layers in a 
desiccator over CaCl2. Purification of KC1 has already been 
noted. It is added to the boric acid solution to bring the salt 
concentration in the borate mixtures to a point comparable with 
that of the phosphate mixtures so that colorimetric checks may 
be obtained with the two series where they overlap. One liter 
of the solution should contain 12.4048 4 grams of boric acid and 
14.912 grams of potassium chlorid. 

M/5 sodium hydroxid solution. This solution is the most diffi- 
cult to prepare, since it should be as free as possible from carbon- 
ate. A solution of sufficient purity for the present purposes may 
be prepared from a high grade sample of the hydroxid in the 
following manner. Dissolve 100 grams NaOH in 100 cc. distilled 
water in a Jena or Pyrex glass Erlenmeyer flask. Cover the 
mouth of the flask with tin foil and allow the solution to stand 
over night till the carbonate has settled. Then prepare a filter 
as follows. Cut a "hardened " filter paper to fit a Buchner funnel. 
Treat it with warm, strong [1:1] NaOH solution. After a few 
minutes decant the sodium hydroxid and wash the paper first 
with absolute alcohol, then with dilute alcohol, and finally with 
large quantities of distilled water. Place the paper on the Buch- 
ner funnel and apply gentle suction until the greater part of the 
water has evaporated; but do not dry so that the paper curls. 
Now pour the concentrated alkali upon the middle of the paper, 
spread it with a glass rod making sure that the paper, under 
gentle suction, adheres well to the funnel, and draw the solution 

* Boric acid begins to lose "water of constitution" above 50°C. 

* This weight was used on the assumption that the atomic weight of 
boron is 11.0. The atomic weight has since been revised and appears as 
10.9 in the 1920 table. 

Because the solutions were standardized with the above weight of boric 
icid this weight should be used. 



102 THE DETERMINATION OF HYDROGEN IONS 

through with suction. The clear filtrate is now diluted quickly, 
after rough calculation, to a solution somewhat more concentrated 
than N/1. Withdraw 10 cc. of this dilution and standardize 
roughly with an acid solution of known strength, or with a sample 
of acid potassium phthalate. From this approximate standardi- 
zation calculate the dilution required to furnish an M/5 solution. 
Make the required dilution with the least possible exposure, and 
pour the solution into a paraffined 5 bottle to which. a calibrated 50 
cc. burette and soda-lime guard tubes have been attached. The 
solution should now be most carefully standardized. One of the 
simplest methods of doing this, and one which should always be 
used in this instance, is the method of Dodge (1915) in which use 
is made of the acid potassium phthalate purified as already 
described. Weigh out accurately on a chemical balance with 
standardized weights several portions of the salt of about 1.6 grams 
each. Dissolve in about 20 cc. distilled water and add 4 drops 
phenol phthalein. Pass a stream of C0 2 -free air through the 
solution and titrate with the alkali till a faint but distinct and 
permanent pink is developed. It is preferable to use a factor 
with the solution rather than attempt adjustment to an exact 
M/5 solution. 

If one should be fortunate enough to find that the concentrated 
sodium hydroxid solution had clarified itself without leaving 
suspended carbonate, the clear solution might be carefully pi- 
petted from the sediment. Cornog (1921) describes another 
method as follows: 

Distilled water contained in an Erlenmeyer flask is boiled to remove 
any carbon dioxide present, after which, when the water is cooled enough, 
ethyl ether is added to form a layer 3 or 4 cm. in depth. Pieces of metallic 
sodium, not exceeding about 1 cm. in diameter are then dropped into the 
flask. They will fall no further than the ether. layer where they remain 
suspended. The water contained in the ether layer causes the slow forma- 
tion of sodium hydroxid, which readily passes below to the water layer. 

8 The author finds that thick coats of paraffine are more satisfactory than 
the thin coats sometimes recommended. Thoroughly clean and dry the 
bottle, warm it and then pour in the melted paraffine. Roll gently to make 
an even coat and just before solidification occurs stand the bottle upright 
to allow excess paraffine to drain to the bottom and there form a very sub- 
stantial layer. 



STANDARD BUFFER SOLUTIONS 103 

Cornog depends upon the evaporation of the ether as a barrier 
to CO2. There are various ways in which the protection can be 
made more sure, and there are also various ways in which the 
aqueous solution may be separated from the ether. 

From time to time there appear in the literature suggestions 
regarding the use of barium salts to remove the carbonate in 
alkali solutions. 

In the author's opinion the next step to take, if the separation 
of carbonate from very concentrated NaOH solutions is not con- 
sidered refined enough for the purpose at hand, is to proceed 
directly to the electrolytic preparation of an amalgam. Given 
a battery and two platinum electrodes this is a simple process. 
A deep layer of redistilled mercury is placed in a conical separa- 
tory funnel. The negative pole of the battery is led to this 
mercury by a glass-protected platinum wire. Over the mercury 
is placed a concentrated solution of recrystallized sodium 
chlorid and in this solution is dipped a platinum electrode con- 
nected with the positive pole of the battery. The battery may 
be 4 to 6 volts. Electrolysis is continued with occasional gentle 
shaking to break up amalgam crystals forming on the mercury 
surface. 

Boil the CO2 out of a litre or so of redistilled water, and, while 
steam is still escaping, stopper the flask with a cork carrying a 
siphon, a soda-lime guard tube and a corked opening for the 
separatory funnel. 

When the water is cool introduce the delivery tube of the separa- 
tory funnel and deliver the amalgam. Allow reaction to take 
place till a portion of the solution, when siphoned off to a 
burette and standardized, shows that enough hydroxid has been 
formed. Then siphon approximately the required amount into a 
boiled-out and protected portion of water. Mix thoroughly and 
standardize. 

M/5 hydrochloric acid solution. Dilute a high grade hydro- 
chloric acid solution to about 20 per cent and distill. Dilute the 
distillate to approximately M/5 and standardize with the sodium 
hydroxid solution previously described. If convenient, it is well 
to standardize this solution carefully by the silver chlorid method 
and check with the standardized alkali. 



104 



THE DETERMINATION OF HYDROGEN IONS 



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Fig. 11. Clark and Lubs' Standard Mixtures 

A. 50 cc. 0.2m KHPhthalate + X cc. 0.2m HC1. Diluted to 200 cc. 

B. 50 cc. 0.2m KHPhthalate + X cc. 0.2m NaOH. Diluted to 200 cc. 

C. 50 cc. 0.2m KH 2 PO< + X cc. 0.2m NaOH. Diluted to 200 cc. 

D. 50 cc. 0.2m H s B0 3 , 0.2m KC1 + X cc. 0.2m NaOH. Diluted to 200 cc. 



STANDARD BUFFER SOLUTIONS 105 

The only solution which it is absolutely necessary to protect 
from the CO2 of the atmosphere is the sodium hydroxid solution. 
Therefore all but this solution may be stored in ordinary bottles 
of resistant glass. The salt solutions, if adjusted to exactly M/5, 
may be measured from clean calibrated pipettes. 

These constitute the stock solutions from which the mixtures 
are prepared. The general relationships of these mixtures to 
their pH values are shown in figure 11. In this figure pH values 
are plotted as ordinates against X cc. of acid or alkali as abscissas. 
It will be found advantageous to plot this figure from table 21 with 
greatly enlarged scale so that it may be used as is S0rensen's 
chart (1909). The compositions of the mixtures at even intervals 
of 0.2 pH are given in table 21. 

In any measurement the apportionment of scale divisions 
should accord with the precision. Scale divisions should not be 
so coarse that interpolations tax the judgment nor so fine as to 
be ridiculous. What scale divisions are best in the method under 
discussion it is difficult to decide, since the precision which may 
be attained depends somewhat upon the ability of the individual 
eye, and upon the material examined, as well as upon the means 
and the judgment used in overcoming certain difficulties which 
we shall mention later. S0rensen (1909) has arranged the stand- 
ard solutions to differ by even parts of the components, a system 
which furnishes uneven increments in pH. Michaelis, (1910) 
on the other hand, makes his standards vary by about 0.3 pH 
so that the corresponding hydrogen ion concentrations are approxi- 
mately doubled at each step. Certain general considerations 
lead to the conclusion that for most work estimation of pH values 
to the nearest 0.1 division is sufficiently precise, and that this 
precision can be obtained when the nature of the medium per- 
mits if the comparison standards differ by increments of 0.2 pH. 

It is convenient to prepare 200 cc. of each of the mixtures and 
to preserve them in bottles each of which has its own 10 cc. 
pipette thrust through the stopper. , It takes but little more time 
to prepare 200 cc. than it does to prepare a 10 cc. portion, and 
if the larger volume is prepared there will not only be a sufficient 
quantity for a day's work but there will be some on hand for the 
occasional test. 

Unless electrometric measurements can be used as control, we 



106 



THE DETERMINATION OP HYDROGEN IONS 



urge the most scrupulous care in the preparation and preserva- 
tion of the standards. We have specified several recrystallizations 
of the salts used because no commercial samples which we have 
yet encountered are reliable. 



TABLE 21 

Composition of mixtures giving pH values at 
KC1-HC1 mixtures* 



\C. at intervals of 0.2 



pH 












1.2 


50 cc. 


M/5 KC1 


64.5 cc. 


M/5 HC1 


Dilute to 200 cc. 


1.4 


50 cc. 


M/5 KC1 


41.5 cc. 


M/5 HC1 


Dilute to 200 cc. 


1.6 


50 cc. 


M/5 KC1 


26.3 cc. 


M/5 HC1 


Dilute to 200 cc. 


1.8 


50 cc. 


M/5 KC1 


16.6 cc. 


M/5 HC1 


Dilute to 200 cc. 


2.0 


50 cc. 


M/5 KC1 


10.6 cc. 


M/5 HC1 


Dilute to 200 cc. 


2.2 


50 cc. 


M/5 KC1 


6.7 cc. 


M/5 HC1 


Dilute to 200 cc. 



* The pH values of these mixtures are given by Clark and Lubs (1916) 
as preliminary measurements. 

Phthalate-HCl mixtures 

2.2 50 cc. M/5 KHPhthalate 46 .70 cc. M/5 HC1 Dilute to 200 cc. 

2.4 50 cc. M/5 KHPhthalate 39.60 cc. M/5 HC1 Dilute to 200 cc. 

2.6 50 cc. M/5 KHPhthalate 32.95 cc. M/5 HC1 Dilute to 200 cc. 

2.8 50 cc. M/5 KHPhthalate 26.42 cc. M/5 HC1 Dilute to 200 cc. 

3.0 ' 50 cc. M/5 KHPhthalate 20.32 cc. M/5 HC1 Dilute to 200 cc. 

3.2 50 cc. M/5 KHPhthalate 14.70 cc. M/5 HC1 Dilute to 200 cc. 

3.4 50 cc. M/5 KHPhthalate 9.90 cc. M/5 HC1 Dilute to 200 cc. 

3.6 50 cc. M/5 KHPhthalate 5 .97 cc. M/5 HC1 Dilute to 200 cc. 

3.8 50 cc. M/5 KHPhthalate 2.63 cc. M/5 HC1 Dilute to 200 cc. 

Phthalate-NaOH mixtures 



4.0 50 cc. M/5 KHPhthalate 0.40 cc. M/5 NaOH Dilute to 200 cc. 

4.2 50 cc. M/5 KHPhthalate 3.70 cc. M/5 NaOH Dilute to 200 cc. 

4.4 50 cc. M/5 KHPhthalate 7.50 cc. M/5 NaOH Dilute to 200 cc. 

4.6 50 cc. M/5 KHPhthalate 12.15 cc. M/5 NaOH Dilute to 200 cc. 

4.8 50 cc. M/5 KHPhthalate 17.70 cc. M/5 NaOH Dilute to 200 cc. 

5.0 50 cc. M/5 KHPhthalate 23.85 cc. M/5 NaOH Dilute to 200 cc. 

5.2 50 cc. M/5 KHPhthalate 29.95 cc. M/5 NaOH Dilute to 200 cc. 

5.4 50 cc. M/5 KHPhthalate 35.45 cc. M/5 NaOH Dilute to 200 cc. 

5.6 50 cc. M/5 KHPhthalate 39.85 cc. M/5 NaOH Dilute to 200 cc. 

5.8 50 cc. M/5 KHPhthalate 43.00 cc. M/5 NaOH Dilute to 200 cc. 

6.0 50 cc. M/5 KHPhthalate 45.45 cc. M/5 NaOH Dilute to 200 cc. 

6.2 50 cc. M/5 KHPhthalate 47.00 cc. M/5 NaOH Dilute to 200 cc. 



STANDARD BUFFER SOLUTIONS 



107 



KH 2 P0 4 -NaOH mixtures 



5.8 
6.0 

6.2 
6.4 
6.6 
6.8 

7.0 
7.2 
7.4 
7.6 
7.8 
8.0 



50 cc 
50 cc 
50 cc 
50 cc, 
50 cc 
50 cc, 
50 cc, 
50 cc, 
50 cc 
50 cc, 
50 cc, 
50 cc 



M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 
M/5 KH 2 P0 4 



3.72 cc. 

5.70 cc. 

8.60 cc. 
12.60 cc. 
17.80 cc. 
23.65 cc. 
29.63 cc. 
35.00 cc. 
39.50 cc. 
42.80 cc. 
45.20 cc. 
46.80 cc. 



M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 



Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 



to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 



Boric acid, KCl-NaOH mixtures 



7.8 50 cc. 
8.0 50 cc. 
8.2 50 cc. 
8.4 50 cc. 
8.6 50 cc. 
8.8 50 cc. 
9.0 50 cc. 
9.2 50 cc. 
9.4 50 cc. 
9.6 50 cc. 
9.8 50 cc. 
10.0 50 cc. 



M/5 H 3 B0 3 
M/5 H3BO3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 
M/5 H 3 B0 3 



M/5KC1 2 
M/5KC1 3 
M/5KC1 5 
M/5KC1 8 
M/5 KC1 12 
M/5KC1 16 
M/5 KC1 21 
M/5KC126 
M/5KC1 32 
M/5 KC1 36 
M/5 KC1 40 
M/5 KC1 43 



61 cc 
97 cc 
90 cc 
50 cc 
00 cc 
30 cc 
30 cc 
70 cc 
00 cc 
85 cc 
80 cc 
90 cc 



M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 
M/5 NaOH 



Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 
Dilute 



to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 
to 200 cc. 



It is important to check the consistency of any particular set 
of these mixtures by comparing "5.8" and "6.2 phthalate" with 
"5.8" and "6.2 phosphate" using brom cresol purple. Also 
"7.8" and "8.0 phosphate" should be compared with the corre- 
sponding borates using cresol red. 

S0rensen's standards are made as follows. The stock solutions 
are: 4 

1. A carefully prepared exact tenth normal solution of HC1. 

2. A carbonate-free exact tenth normal solution of NaOH. 

3. A tenth molecular glycocoll solution containing sodium chlo- 
rid, 7.505 grams glycocoll and 5.85 grams NaCl in 1 litre of 
solution. 

4. An M/15 solution of primary potassium phosphate which 
contains 9.078 grams KH 2 P0 4 in 1 litre of solution. 



108 



THE DETERMINATION OF HYDROGEN IONS 



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Fia. 12. S0rensen's Standard Mixtures, Walpole's Acetate Solutions 

AND PALITZSCH's BORATE SOLUTIONS 

Mixtures of A parts of acid constituent and B parts of basic constituent. 



STANDARD BUFFER SOLUTIONS 109 

5. An M/15 solution of secondary sodium phosphate which 
contains 11.876 grams Na 2 HP04,2H 2 in 1 litre of solution. 

6. A tenth molecular solution of secondary sodium citrate made 
from a solution containing 21.008 grams crystallized citric acid 
and 200 cc. carbonate-free N/1 NaOH diluted to 1 litre. 

7. An alkaline borate solution made from 12.404 grams boric 
acid dissolved in 100 cc. carbonate-free N/1 NaOH and diluted 
to 1 litre. 

The materials for these solutions are described by S0rensen as 
follows. 

The water shall be boiled, carbon dioxid-free, distilled water, 
and the solutions shall be protected against contamination by 
C0 2 . 

Glycocoll (Glycine) 

Two grams glycocoll should give a clear solution in 20 cc. 
water and should test practically free of chlorid or sulfate. Five 
grams should yield less than 2 mgm. of ash. Five grams should 
yield, on distillation with 300 cc. of 5 per cent sodium hydroxid, 
less than 1 mgm. of nitrogen as ammonia. The nitrogen content 
as determined by the Kjeldahl method should be 18.67 ±0.1 per 
cent. 

Primary phosphate, KH2PO4 

The salt must dissolve clear in water and yield no test for chlo- 
rid or for sulfate. When dried under 20 or 30 mm. pressure for 
a day at 100°C. the loss in weight should be less than 0.1 per cent, 
and on ignition the loss should be 13.23 ±0.1 per cent. When 
compared colorimetrically with citrate mixtures the stock phos- 
phate solution should lie between "7" and "8 citrate-HCl." On 
addition of a drop of tenth-normal alkali or acid to 100 cc. the 
color of this phosphate solution with an indicator should be 
widely displaced. 

Secondary phosphate, Na 2 HP04, 2H 2 

The salt with this content of water of crystallization is pre- 
pared by exposing to the ordinary atmosphere the crystals con- 



110 THE DETERMINATION OF HYDROGEN IONS 

taining twelve mols of water. 6 About two weeks exposure is 
generally sufficient. The salt should dissolve clear in water and 
yield no test for chlorid or sulfate. A day of drying under 20 to 
30 mm. pressure at 100°C. and then careful ignition to constant 
weight, should result in a 25.28 ± 0.1 per cent loss. The stock 
solution should correspond on colorimetric test with "10 borate- 
HC1" and should be displaced beyond "8 borate-HCl" on addi- 
tion of a drop of N/10 acid, and beyond "8 borate-NaOH " with 
a drop of alkali to 100 cc. 

Citric acid, C6H 8 07,H 2 

The acid should dissolve clear in water, should yield no test for 
chlorid or sulfate and should give practically no ash. The water 
of crystallization may be determined by drying under 20 to 30 
mm. pressure at 70° C. On drying in this manner the acid should 
remain colorless and lose 8.58 ± 0.1 per cent. The acidity of the 
citric acid solution is determined by titration with 0.2 N barium 
hydroxid with phenolphthalein as indicator. Titration is carried 
to a distinct red color of the indicator. 

Boric acid, H 3 B0 3 

Twenty grams of boric acid should go completely into solution 
in 100 cc. of water when warmed on a strongly boiling water bath. 
This solution is cooled in ice water and the filtrate from the crys- 
tallized boric acid is tested as follows. It should give no tests for 
chlorides or sulfates. It should be orange to methyl orange. A 
drop of N/10 HC1 added to 5 cc. should make the filtrate red 
to methyl orange. Twenty cubic centimeters of the filtrate evap- 
orated in platinum, treated with about 10 grams of hydrofluoric 
acid and 5 cc. of concentrated sulfuric acid and reevaporated, 
ignited and weighed, should yield less than 2 mgm. when corrected 
for non-volatile matter in the HF. 

fne following tables give the S0rensen mixtures with the cor- 
responding pH values. Mixtures whose pH values are consid- 

• Certain samples of secondary sodium phosphate sold for the prepa- 
ration of buffer standards and called "S0rensen's Phosphate" are wrongly 
labeled Na 2 HP0 4 . 



STANDARD BUFFER SOLUTIONS 



111 



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5.5 Glycine + 4.5 NaOH 

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112 



THE DETERMINATION OF HYDROGEN IONS 





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TABLE 24 
Stfrensen's borate — HCl mixtures after W album 





10° 


20° 


30° 


40° 


50° 


60° 


70° 






10.0 Borate 


9.30 
9.22 


9.23 
9.15 


9.15 

9.08 


9.08 
9.01 


9.00 
8.94 


8.93 

8.87 


8.86 


9.5 Borate + 0.5 HCl 


8.80 


9.0 Borate + 1.0 HCl 


9.14 


9.07 


9.01 


8.94 


8.87 


8.80 


8.74 


8.5 Borate + 1.5 HCl 


9.06 


8.99 


8.92 


8.86 


8.80 


8.73 


8.67 


8.0 Borate + 2.0 HCl 


8.96 


8.89 


8.83 


8.77 


8.71 


8.65 


8.59 


7.5 Borate + 2.5 HCl 


8.84 


8.79 


8.72 


8.67 


8.61 


8.55 


8.50 


7.0 Borate + 3.0 HCl 


8.72 


8.67 


8.61 


8.56 


8.50 


8.45 


8.40 


6.5 Borate + 3.5 HCl 


8.54 


8.49 


8.44 


8.40 


8.35 


8.30 


8.26 


6.0 Borate + 4.0 HCl 


8.32 


8.27 


8.23 


8.19 


8.15 


8.11 


8.08 


5.75 Borate + 4.25 HCl... 


8.17 


8.13 


8.09 


8.06 


8.02 


7.98 


7.95 


5.5 Borate + 4.5 HCl 


7.96 


7.93 


7.89 


7.86 


7.82 


7.79 


7.76 


5.25 Borate + 4.75 HCl... 


7.64 


7.61 


7.58 


7.55 


7.52 


7.49 


7.47 



TABLE 25 
Sflrensen's citrate — NaOH mixtures after Walbum 



Temperature. 



10.0 Citrate 

9.5 Citrate + 0.5 NaOH.. 
9.0 Citrate + 1.0 NaOH.. 
8.0 Citrate + 2.0 NaOH.. 
7.0 Citrate + 3.0 NaOH.. 
6.0 Citrate + 4.0 NaOH.. 
5.5 Citrate + 4.5 NaOH.. 
5.25 Citrate + 4.75 NaOH 



10° 


20° 


30° 


4C° 


50° 


60° 


4.93 


4.96 


5.00 


5.04 


5.07 


5.10 


4.99 


5.02 


5.06 


5.10 


5.13 


5.16 


5.08 


5.11 


5.15 


5.19 


5.22 


5.25 


5.27 


5.31 


5.35 


5.39 


5.42 


5.45 


5.53 


5.57 


5.60 


5.64 


5.67 


5.71 


5.94 


5.98 


6.01 


6.04 


6.08 


6.12 


6.30 


6.34 


6.37 


6.41 


6.44 


6.47 


6.65 


6.69 


6.72 


6.76 


6.79 


6.83 



70° 



5.14 
5.20 
5.29 
5.49 
5.75 
6.15 
6.51 
6.86 



TABLE 26 
irensen's glycocoll — HCl mixtures 



GLYCOCOLL 


HCl 


pH 


CC. , 


CC. 




0.0 


10.0 


1.038 


1.0 


9.0 


1.146 


2.0 


8.0 


1.251 


3.0 


7.0 


1.419 


4.0 


6.0 


1.645 


5.0 


5.0 


1.932 


6.0 


4.0 


2.279 


7.0 


3.0 


2.607 


8.0 


2.0 


2.922 


9.0 


1.0 


3.341 


9.5 


. 0.5 


3.679 



113 



114 



THE DETERMINATION OF HYDROGEN IONS 



TABLE 27 

irensen's phosphate mixtures 



SECONDARY 


PRIMARY 


pH 


CC. 


CC. 




0.25 


9.75 


5.288 


0.5 


9.5 


5.589 


1.0 


9.0 


5.906 


2.0 


8.0 


6.239 


3.0 


7.0 


6.468 


4.0 


6.0 


6.643 


5.0 


5.0 


6.813 


6.0 


4.0 


6.979 


7.0 


3.0 


7.168 


8.0 


2.0 


7:381 


9.0 


1.0 


7.731 


9.5 


0.5 


8.043 



TABLE 28 
S0rensen's citrate — HCl mixtures 



CITRATE 


HCl 


pH 


CC. 


CC. 




0.0 


10.0 


1.038 


1.0 


9.0 


1.173 


2.0 


8.0 


1.418 


3.0 


7.0 


1.925 


3.33 


6.67 


2.274 


4.0 


6.0 


2.972 


4.5 


5.5 


3.364 


4.75 


5.25 


3.529 


5.0 


5.0 


3.692 


5.5 


4.5 


3.948 


6.0 


4.0 


4.158 


7.0 


3.0 


4.447 


8.0 


2.0 


4.652 


9.0 


1.0 


4.830 


9.5 


0.5 


4.887 


10.0 


0.0 


4.958 



STANDARD BUFFER SOLUTIONS 



115 



TABLE 29 

Walpole's acetate buffer mixtures, recalculated for intervals of 0.2 pH. 
acetate 0.2 molecular 



Total 



PH 


CONCENTRATION (MOLALITY) 




Acetic Acid 


Sodium acetate 


3.6 
3.8 

4.0 
4.2 
4.4 
4.6 
4.8 
5.0 
5.2 
5.4 
5.6 


0.185 
0.176 
0.164 
0.147 
0.126 
0.102 
0.080 
0.059 
0.042 
0.029 
0.019 


0.015 
0.024 
0.036 
0.053 
0.074 
0.098 
0.120 
0.141 
0.158 
0.171 
0.181 



TABLE 30 

Palitzsch's borax-boric acid mixtures 



M/20 BORAX 


M/5 boric acid, M/20 NaCl 


pH 


cc. 


cc. 




10.0 


0.0 


9.24 


9.0 


1.0 


9.11 


8.0 


2.0 


8.98 


7.0 


3.0 


8.84 


6.0 


4.0 


8.69 


5.5 


4.5 


8.60 


5.0 


5.0 


8.51 ' 


4.5 


5.5 


8.41 


4.0 


6.0 


8.31 


3.5 


6.5 


8.20 


3.0 


7.0 


8.08 


2.5 


7.5 


7.94 


2.3 


7.7 


7.88 


2.0 


8.0 


7.78 


1.5 


8.5 


7.60 


1.0 


9.0 


7.36 


0.6 


9.4 


7.09 


0.3 


9.7 


6.77 



116 



THE DETERMINATION OF HYDROGEN IONS 



ered by S0rensen to be too uncertain and which he has indicated 
by brackets are omitted in these tables. The third decimal of 
S0rensen's tables are given by S0rensen in small type. 



TABLE 31 
Mcllvaine's standards 



pH REQUIRED 


0.2MNa 2 HPO< 


0.1 M CITRIC ACID 




cc. 


CC. 


2.2 


0.40 


19.60 


2.4 


1.24 


18.76 


2.6 


2.18 


17.82 


2.8 


3.17 


16.83 


3.0 


4.11 


15.89 


3.2 


4.94 


15.06 


3.4 


5.70 


14.30 


3.6 


6.44 


13.56 


3.8 


7.10 


12.90 


4.0 


7.71 


12.29 


4.2 


8.28 


11.72 


4.4 


8.82 


11.18 


4.6 


9.35 


10.65 


4.8 


9.86 


10.14 


5.0 


10.30 


9.70 


5.2 


10.72 


9.28 


5.4 


11.15 


8.85 


5.6 


11.60 


8.40 


5.8 


12.09 


7.91 


6.0 


12.63 


7.37 


6.2 


13.22 


6.78 


6.4 


13.85 


6.15 


6.6 


14.55 


5.45 


6.8 


15.45 


4.55 


7.0 


16.47 


3.53 


7.2 


17.39 


2.61 


7.4 


18.17 


1.83 


7.6 


18.73 


1.27 


7.8 


19.15 


0.85 


8.0 


19.45 


0.55 



Walbum (1920) has determined the pH values for the S0ren- 
sen mixtures at temperatures of 10°, 18°, 28°, 37°, 46°, 62° and 
70°C. and has interpolated data for intervening temperatures. 
He uses a system of reference essentially that which is described 



STANDARD BUFFER SOLUTIONS 117 

in Chapter XIX as standard. He finds that upon this basis the 
alteration of pH with temperature is for the most part negligible 
for the phosphate mixtures, the glycocoll-HCl mixtures and the 
citrate-HCl mixtures. Data for the other mixtures are tabu- 
lated in tables 22, 23, 24 and 25. In these will be found S0ren- 
sen's values at 18°. Tables 26, 27 and 28 are taken from 
S0rensen's paper of 1912. 

The stock solutions for the Palitzsch mixtures given in table 30 
are an M/20 Borax solution containing 19.108 grams 7 Na 2 B 4 07 
10H 2 O in 1 litre; and an M/5 Boric acid, NaCl solution contain- 
ing 12.404 grams 7 H 3 B0 3 and 2.925 grams NaCl in 1 litre. 

Mcllvaine (1921) has given the electrometrically determined 
pH values for a series of mixtures of 0.2 M disodium phosphate 
and 0.1 M citric acid. Since the citrate exerts a buffer action 
at the steep part of the phosphate curve near the position where 
the mono alkali phosphate alone is present Mcllvaine's mixtures 
give a continuous buffer action from pH 2.2 to pH 8.0. His data 
are shown in table 31. 

Acree and his coworkers have published curves for other mix- 
tures giving more or less smooth slopes over wide ranges of pH. 

Kolthoff in his 1921 text has recalculated the follow, ing data 
from Ringer (1909): 

TABLE 32 
Ringer's mixtures of 0.15M Na 2 HPOi and 0.1M NaOH 



50 cc. Na 2 HP0 4 + 15 cc. NaOH. 
50 cc. Na 2 HP0 4 + 25 cc. NaOH. 
50 cc. Na 2 HP0 4 + 50 cc. NaOH. 
50 cc. Na 2 HP0 4 + 75 cc. NaOH. 



pH 



10.97 
11.29 
11.77 
12.06 






7 The values given by Palitzsch were calculated upon the basis of 11.0 
as the atomic weight of boron. Since this was the value used, the new 
value of 10.9 given in the atomic weight table in 1 he report of the inter- 
national committee for 1922 should not be used in calculating the composi- 
tion of the specific solutions given by Palitzsch. 



CHAPTER VII 

Sources of Error in Colorimetric Determinations 

There are errors of technique such as incorrect apportionment 
of the indicator concentration in tested and standard solution and 
the use of unequal depths of solutions through which the colors 
are viewed that may be passed over with only a word of reminder. 
Likewise we may recall certain of the optical effects mentioned 
in Chapter IV and then pass on to the more serious difficulties 
in the application of the indicator method. 

In the comparison of electrometric and colorimetric measure- 
ments discrepancies have often been traced so clearly to two defi- 
nite sources of error that they have been given categorical dis- 
tinction. They are the so-called "protein" and "salt" errors. 

From what has already been said in previous pages, it will 
be seen that, if there are present in a tested solution bodies which 
remove the indicator or its ions from the field of action either by 
adsorption , or otherwise, the equilibria which have formed the 
basis of our treatment will be disturbed. An indicator in such a 
solution may show a color intensity, or even a quality of color, 
which is different from that of the same concentration of the indi- 
cator in a solution of the same hydrogen ion concentration where 
no such disturbance occurs. We could easily be led to attribute 
very different hydrogen ion concentrations to the two solutions. 
This situation is not uncommon when we are dealing with protein 
solutions, for in some instances there is distinctly evident the re- 
moval of the indicator from the field. In other cases the discrep- 
ancy between electrometric and colorimetric measurements is not 
so clear, nor can it always be attributed solely to the indicator 
measurement. 

If two solutions of inorganic material, each containing the same 
concentration of hydrogen ions,' are tested with an indicator, we 
should expect the same color to appear. If, however, these two 
solutions have different concentrations of salt, it may happen that 
the indicator color is not the same. As S0rensen (1909) and 
Scfrensen and Palitzsch (1913) have demonstrated, this effect of 

118 



ERRORS IN COLORIMETR1C DETERMINATIONS 



119 



the salt content of a solution cannot be tested by adding the salt 
to one of two solutions which have previously been brought to 
the same hydrogen ion concentration. The added salt, no matter 
if it be a perfectly neutral salt, will change either the hydrogen 
ion concentration or the hydrogen ion activity of the solution or 
so affect the electrode equilibrium that it appears as if the hydro- 
gen ion activity is altered. 

So long as hydrogen electrode measurements are made the 
standard it is convenient to throw the burden of the "salt effect" 
upon the indicator; but neutral salts are known to displace elec- 
trode potential differences from the point estimated from the 
expected hydrogen ion concentration. Tentatively we may deal 
with the salt effect as if the hydrogen electrode measurement 
were the point of reference, and this will doubtless harmonize 
with future developments of theory. 

Bjerrum (1914) gives an example of a case where the influence 
}f the neutral salt is evidently upon the buffer equilibrium rather 
;han on the indicator. An ammonium-ammonium salt buffer 
nixture and a borate buffer mixture are both made up to the 
name color of phenolphthalein. On the addition of sodium chlo- 
ride the color of phenolphthalein becomes stronger in the ammo- 
nium mixture and weaker in the borate mixture. 

The following table taken from Prideaux (1917) illustrates the 
order of magnitude of the "salt error" in some instances. 



INDICATOR 



] ara benzene sulphonic acid azo naphthylamine. 

I ara nitro phenol 

/ lizarine sulphonic acid 

1 eutral red 

I osolic acid 

I ara benzene sulphonic acid azo a-naphthol . . . 
I henolphthalein 



BUFFER USED 



Phosphate 
Phosphate 
Phosphate 
Phosphate 
Phosphate 
Phosphate 
Phosphate 



CHANGE OF pH 

IN PRESENCE OF 

0.5 N NaCl 



-0.10 
+0.15 
+0.26 
-0.09 
+0.08 
+0.12 
+0.12 



\ In cases where the solutions under examination are of the same 
g meral nature hydrogen electrode measurements may be taken as 
t te standard and colorimetric measurements calibrated accord- 
i gly. S0rensen and Palitzsch (1910) did this in their study of 



120 



THE DETERMINATION OF HYDROGEN IONS 



the salt errors of indicators in sea water. They acidified the sea 
water and passed hydrogen through to displace carbon dioxid, 
and then neutralized it to the ranges of various indicators with 
buffer mixtures and compared colorimetric with electrometric 
measurements. In this way they found the following deviations. 



INDICATOR 


BUFFER 


PARTS PER 1000 OF SALTS AND 
CORRESPONDING ERRORS 




35 


20 


5 


l 


Faranitro phenol 


Phosphate 

Phosphate 

Borate 

Phosphate 

Borate 


+0.12 
-0.10 
+0.22 
+0.16 
+0.21 


+0.08 
-0.05 
+0.17 
+0.11 
+0.16 




+0.03 
-0.04 
+0.05 




Neutral red 





a-Napththol phthalein..\ 
Phenolphthalein 


-0.07 
-0.14 
-0.03 







If, for example, sea water of about 3.5 per cent salt is matched 
against a standard borate solution with phenolphthalein and 
appears to be pH 8.43 the real value is pH 8.22. 

Such calibration is doubtless the very best way to deal with the 
salt errors since it tends to bring measurements to a common 
experimental system of reference. 

Kolthoff (1922) gives the following table showing the correc- 
tions to be applied for the "salt error" of various indicators. It 
should be noted that Kolthoff includes in this table data obtained 
when the hydrogen electrode potentials were taken as standard 
and also data in which the pH values were calculated. The two 
sets are not strictly comparable (see Chapter XIX) and there- 
fore must be used with caution in theoretical work. We have 
eliminated from Kolthoff's table Congo red, Azolitmin, and 
Tropaeolin O (Chrysom) which Kolthoff describes as having 
salt errors so large that these indicators are useless. 

Michaelis and his coworkers have determined the salt errors 
for a number of the nitrophenols, but, since the corrections are 
often intimately related to the constants used in Michaelis* 
method of operating, the reader is referred to the original litera- 
ture for the details. See Chapter VIII. 

The reader was warned in Chapter II that the treatment to be 
given the so-called salt errors of indicators would not deal with the 
theory. There are various theories that have been advanced, 



TABLE 33 

Salt error of indicators, after Kolthoff 



INDICATOR 



Tropaeolin 00 
(Orange IV) 



Methyl orange 
Butter yellow. . 



Thymol blue (acid 
range) 



Brom phenol blue < 

Brom cresol purple. 
Phenol red 



Thymol blue 

Methyl red 

p-Nitro phenol.. . 
Azo yellow 3G. . . 
Phenolph thalein . 

Nitramine (?)... 



SALT 


SALT 
CONCEN- 
TRATION 


CORREC- 
TION 


KC1 


0.10 N 


-0.05 


KC1 


0.25 N 


-0.01 


KC1 


0.50 N 


+0.06 


KC1 


1.00 N 


+0.23 


KC1 


0.10 N 


-0.08 


KC1 


0.25 N 


-0.08 


KC1 


0.50 N 


+0.02 


KC1 


1.00 N 


+0.23 


KC1 


0.10 N 


-0.08 


KC1 


0.10 N 


-0.06 


KC1 


0.20 N 


-0.06 


KC1 


0.50 N 


-0.04 


KC1 


1.00 N 


+0.05 


KC1 


0.10 N 


-0.05 


KC1 


0.25 N 


-0.15 


KC1 


0.50 N 


-0.35 


KC1 


1.00 N 


-0.35 


NaCl 


0.50 N 


-0.25 


NaCl 


0.50 N 


-0.15 


NaCl 


0.50 N 


-0.17 


NaCl 


0.50 N 


+0.10 


NaCl 


0.50 N 


-0.05 


NaCl 


0.50 N 


0.00 


NaCl 


0.50 N 


-0.17 


KC1 


0.10 N 


-0.06 


KC1 


0.25 N 


-0.12 


KC1 


0.50 N 


-0.10 


KC1 


1.00 N 


-0.29 



REMARKS 



Indicator suitable. NaCl 
has about same influence 



Indicator suitable. NaCl 
has about same influence 



Same errors as methyl 
orange but indicator floc- 
culates with salt 

NaCl has same influence 



Corrections large at weaker 
concentration of salt 



At small concentrations of 
salt correction of opposite 
sign 



NaCl has about same influ- 
ence 



121 



122 THE DETERMINATION OF HYDROGEN IONS 

but up to a recent time none has been entirely satisfactory. 
Whether the newer concepts of the conduct of strong electrolytes 
will furnish a basis for the correlation of experimental data remains 
to be seen. This much at least will be demanded, that the habit 
of indiscriminately jumbling together dissociation constants and 
other data obtained by widely different methods and bearing 
different implications shall cease. Until a thoroughly consistent 
method of approach and of calculation is accomplished and its 
value established, the only safe procedure to follow is to calibrate 
salt errors by experimental hydrogen electrode measurements. 

In dealing with protein solutions calibration is less certain. 
When solutions to be tested vary greatly, not only in protein con- 
tent but also in the composition and concentration of their salt 
content, systematic calibration becomes very difficult. When 
there are added the difficulties presented by strong coloration 
and turbidity, calibration is impossible. Such is the situation to 
be faced when dealing with the media and the cultures which 
the bacteriologist must handle. 

It is sometimes helpful to construct titration curves of a solu- 
tion under examination, making measurements after addition of 
graded quantities of acid and alkali, in one case with the hydrogen 
electrode and in the other case with indicators, preferably indi- 
cators of different types. The indicator readings may then reveal 
breaks not to be expected from the hydrogen ion relations of the 
solution. If, however, no comparison is made with hydrogen 
electrode measurements, the observer must rely to a considerable 
extent upon his judgment. "Protein errors" are generally the 
larger the more complex and concentrated the protein and tend 
to decrease with increase in the extent of protein hydrolysis. 

There seems to be no way then to deal with either the protein 
or the salt error of indicators but to rely upon the use of those 
indicators which give relatively small errors, to keep in mind the 
order of magnitude of the error to be expected from the general 
nature of the solution tested, and, in important cases, to standard- 
ize to the electrometric basis as an arbitrary provisional standard. 

Because of the great variety of solutions tested by the colori- 
metric method it is impracticable to give a condensed statement 
of the probable errors. Elaborate tables of colorimetric and 
electrometric comparisons are given by S0rensen (1909) for the 



ERRORS IN COLORIMETRIC DETERMINATIONS 123 

cases he studied. Clark and Lubs (1917) have tabulated their 
results with the sulphonphthalein indicators. 

In the work of Michaelis or that of Kolthoff salt corrections 
are for the most part established by means of hydrogen electrode 
measurements. Wells (1920) has tabulated some data for cresol 
red in a manner useful for a certain type of water study (cf. Mc- 
Clendon 1917), and Brightman, Meacham and Acree (1920) have 
recorded the effects of different concentrations of phosphate 
buffer. 

The "protein error" and the "salt error" have been given 
prominence in the literature partly because both have to be taken 
into consideration in dealing with biological solutions, and partly 
because there is to be perceived underlying the salt error a most 
interesting phenomenon of rather general interest. However, 
this emphasis should not obscure the fact that there are specific 
conditions for each indicator which render that indicator useless 
for the determination of pH. For instance alizarine, in passing 
from the phosphate to the borate buffer mixtures exhibits a sudden 
transition which has all the appearances of a specific effect of the 
borate upon the indicator. And alizarine is not alone in this 
peculiarity. This same alizarine in the presence of aluminium 
may form a lake and with proper pH control may be made a use- 
ful reagent for aluminium in place of a very poor acid-base indica- 
tor. Zoller (1921) has called attention to the incompatibility 
between certain dyes and the phthalate buffers. Many indica- 
tors are easily reduced or like methyl red easily reduced and then 
so altered that the reduction is irreversible. A number of indi- 
cators undergo their color changes slowly or else fade and are 
lost to the observer. Other indicators precipitate with certain 
cations, for instance Orange IV and Congo with alkali earths. 
In short all possibilities must be watched lest the investigator, 
venturing upon the study of some new solution, be misled by the 
mark of reliability placed upon an indicator tried under limited 
circumstances. 

Wherever possible it is good practice to test doubtful cases 
with two indicators of widely different chemical composition. 

As to the effect of temperature variation, comparatively little 
work has been done. Gillespie and others have some notes on 
the subject and more recently Michaelis and his coworkers have 



124 



THE DETERMINATION OF HYDROGEN IONS 



included temperature data in stating the constants used in the 
Michaelis and Gyemant method (see Chapter VIII). Kolthoff 
(1921) has extended the theory of School in which account is 
taken of the acidic or basic nature of an indicator, but there often 
remains some question as to how a given indicator is to be classi- 
fied. Kolthoff using the values of Kohlrausch and Heydweiller 
for the dissociation constant of water at various temperatures 
has reduced his observations to the following table. In this 



TABLE 34 
Displacement of indicator exponent between 18°C. and 70°C. after Kolthoff 



INDICATOR 



Nitramine 

Phenol phthalein 

Thymol blue, alkaline range 

a-naphthol phthalein 

Curcumine 

Phenol red 

Neutral red 

Brom cresol purple. 

Azolitmin 

Methyl red 

Lacmoid 

p-nitro phenol 

Methyl orange 

Butter yellow 

Bromphenol blue 

Tropaeolin 00 

Thymol blue, acid range . . 



pH DIS- 
PLACEMENT 



-1.45 
-0.9 to 0.4 
-0.4 
-0.4 
-0.4 
-0.3 
-0.7 

0.0 

0.0 
-0.2 
-0.4 
-0.5 
-0.3 
-0.18 

0.0 
-0.45 

0.0 



pOH DISPLACE- 
MENT 



0.0 
-0.55 to 1.05 
-1.05 
-1.05 
-1.05 
-1.15 
-0.75 
-1.45 
-1.45 
-1.25 
-1.05 
-0.95 
-1.15 
-1.17 
-1.45 
-1.0 
-1.45 



RATIO OF 
DISSOCIATION 
CONSTANT AT 

70°C. TO THAT 
AT ORDINARY 

TEMPERATURE 



1.0 
About 5 
2.5 
2.5 
2.5 
2.0 

1.0 
1.0 

2.5 

3.2 
14.0 
15.0 

1.0 
10.0 

1.0 



table the displacement of —0.4 for thymol blue means that if 
thymol blue in a solution at 70°C. shows the same color as the 
same concentration of this indicator in a buffer of pH 9.4 at 
ordinary temperature then the pH of the solution at 70°C. is 9.0. 
Corrections for temperatures between room temperature and 
70 C C. may be interpolated from the data in the table. 



ERRORS IN COLORIMETRIC DETERMINATIONS 125 

REFERENCES 

Abegg-Bose (1899), Arrhenius (1899), Bjerrum (1914), Brightman-Meacham 
Acree (1920), Chow (1920), Clark-Lubs (1917), Dawson-Powis (1913), 
Gillespie-Wise (1918), Harned (1915), Kolthoff (1916, 1918, 1922), 
Lewis (1912), McBain-Coleman (1914), McBain-Salmon (1920), 
Michaelis (1920-21), Michaelis-Gyemant (1920), Michaelis-Kruger 
(1921), Michaelis-Rand (1909), Palmaer-Melander (1915), Poma 
(1914), Poma-Patroni (1914), Prideaux (1917), Rosenstein (1912), 
Sackur (1901), SpTensen (1909), S0rensen-Palitzsch (1910), (1913), 
Wells (1920), Zoller (1921). 
See also Chapter II and page 341. 



CHAPTER VIII 
Approximate Determinations with Indicators 

If you can measure that of which you speak, and can express it by 
a number, you know something of your subject; but if you cannot 
measure it, your knowledge is meagre and unsatisfactory. — Lord 
Kelvin 

The distinctive advantages of the indicator method are the 
ease and the rapidity with which the approximate hydrogen ion 
concentration of a solution may be measured. The introduction 
of improved indicators, the charting of their pH ranges, better 
definition of degree in "acidity" or "alkalinity," and the illumina- 
tion of the theory of acid-base equilibria have developed among 
scientific men in general an appreciation of how indefinite were 
those old, favorite terms — "slightly acid," "distinctly alkaline," 
and "neutral." There is now a clear recognition of the distinct 
difference between quantity and intensity o'f acidity; and for 
each aspect there may be given numerical values admitting 
no misunderstanding. 

Furthermore the clarification of the subject has brought a 
perspective which may show where accuracy is unnecessary and 
where fair approximation is desirable. In such a case the investi- 
gator turns to the indicator method knowing that even if his 
results are rough they can still be expressed in numerical values 
having a definite meaning to others. 

Now a very good approximation may be attained by color 
memory and without the aid of the standard buffer solutions 
or of the systems presently to be described in which the standard 
buffer solutions are dispensed with. 

To establish a color memory as well as to refresh it a set of 
"permanent" standards is convenient. These may be prepared 
with the standard buffer solutions in the ordinary way, protected 
against mold growth by means of a drop of toluol, and sealed 
by drawing off the test tubes in a flame or by corking with the 
cork protected by tinfoil or paraffme. For exhibition purposes 
long homeopathic vials make a very good and uniform container. 
They may be filled almost to the brim and a cork inserted, if a 

126 



APPROXIMATE INDICATOR METHODS 127 

slit is made for the escape of excess air and liquid. The slit may 
then be sealed with paraffine. A hook of spring-brass snapped 
about the neck makes a support by which the vial may be fastened 
to an exhibition board. A neater container is the so-called typhoid- 
vaccine ampoule which is easily sealed in the flame. 

If one of a series of standards so prepared should alter, the 
change can generally be detected by the solution falling out of 
the proper slope of color gradation. But if all in a series should 
change, it may be necessary to Gompare the old with new stand- 
ards. Because such changes do occur, "permanent" standards 
are to be used with caution. The sulfon phthalein indicators 
make fairly permanent standards but the methyl red which is an 
important member of the series of indicators recommended by 
Clark and Lubs (1917) often deteriorates within a short time. 

A device which furnishes a color standard to be interpreted by 
means of a dissociation curve is the color wedge of Bjerrum (1914). 
This is a long rectangular box with glass sides and a diagonal glass 
partition which divides the interior into two equal wedges. One 
compartment contains a solution of the indicator fully transformed 
into its alkaline form, the other a like concentration of the indi- 
cator transformed to the acid form. A view through these wedges 
should imitate the view of a like depth and concentration of the 
indicator transformed to that degree which is represented by the 
ratio of wedge thicknesses at the point under observation. 
Compare Barnett and Barnett (1920) and Myers (1922). 

As an aid to memory the dissociation curves of the indicators 
are helpful even when used alone. The color chart shown in 
Chapter III is a still better aid to memory and within the limita- 
tions mentioned the colors may be used as rough standards. 

Sonden (1921) has used colored glasses and Kolthoff (1922) 
inorganic salt solutions as color standards. 

Colorimetric determination of hydrogen ion concentration without 
the use of standard buffer solutions 

We have already seen that if an indicator is an acid, its degree 
of dissociation, a, is related to the hydrogen ion concentration 
of the solution by the equation 

[H+] = K a 1 -^^ 



128 THE DETERMINATION OF HYDROGEN IONS 

We have also seen that if Ka, the true dissociation constant 
is replaced by the so-called apparent dissociation constant, Ki A , 
which is a function of Ka and of the constants of tautomeric 
equilibria, then a represents the degree of color transformation. 
We then have 

[H+] = K IA ^— ^ 



or the more convenient form 



pH = log — - + log 



K " °1 



a 



where a may now be considered as to the degree of color trans- 
formation. If, for instance, an indicator conducts itself as a simple 
acid with apparent dissociation constant 1 X 10~ 6 , we can con- 
struct the dissociation curve with its central point of inflection at 
pH 6, and then, assuming that this curve represents the relation 
of the percentage color transformation to pH, we can determine 
the pH of a solution if we can determine the percentage color 
transformation which this indicator displays in a tested solution. 
Proceeding on these simple and often unjustified assumptions 
we can now devise a very simple way of detecting the percentage 
color transformation. The following is quoted from Gillespie 
(1920) : 

We may assume that light is absorbed independently by the two forms 
of the indicator, and hence that the absorption, and in consequence of this 
the residual color emerging, will be the same whether the two forms are 
present together in the same solution or whether the forms are separated 
for convenience in two different vessels and the light passes through one 
vessel after the other. Therefore, if we know what these percentages are 
for a given indicator in a given buffer mixture, we can imitate the color 
shown in the buffer mixture by dividing the indicator in the proper pro- 
portion between two vessels, and putting part of it into the acid form with 
excess of acid, the rest into the alkaline form with excess of alkali. 

Gillespie sets up in the comparator (see page 70) two tubes, 
one of which contains, for example, three drops of a given indicator 
fully transformed into the acid color, and the other of which con- 
tains seven drops of the indicator fully transformed into the alka- 
line form. The drop ratio 3 : 7 should correspond to the ratio of 
the concentrations of acid and alkaline forms of ten drops of the 



APPROXIMATE INDICATOR METHODS 129 

indicator in a solution of that pH which is shown by the disso- 
ciation curve of the indicator to induce a seventy per cent trans- 
formation. If then the two comparison tubes and the tested 
solution are kept at the same volume, and the view is through 
equal depths of each, a matching of colors should occur between 
the virage of the two superposed comparison tubes and that of 
the tested solution. 

Barnett and Chapman (1918) applied this method with 
one indicator phenol red but without using the dissociation 
curve. Gillespie (1920) extended the procedure to several other 
indicators and made use of the dissociation curves so that he 
was able to smooth out to more probable values the experimental 
data relating drop ratios to pH. This is important because 
the experimental error in judging color is not inconsiderable 
and if the purely empirical data be made the sole basic standardi- 
zation of the method there may be involved a systematic error, 
which, added to the error of the individual measurement may 
make the cumulative error unnecessarily large. That this had 
already occurred was indicated by Gillespie's comparison of 
the values for the drop ratios of phenol red given by Barnett and 
Chapman on the one hand and the report of the bacteriologists' 
committee (Conn, et al., 1919) on the other hand. 

Gillespie found the correspondence between the experimental 
and the theoretical results predicted on the basis of the simpli- 
fying assumptions mentioned above to be very good for the sul- 
fon phthaleins, doubtless because of the reasons mentioned in 
Chapter IV. He also showed good correspondence in the case 
of methyl red but reiterates the fact that phenol phthalein cannot 
be treated by means of the simple dissociation curve for a mono 
acidic acid, as was mentioned in Chapter IV. 

In table 35 are given the pH values corresponding to various 
drop ratios of seven indicators as determined by Gillespie. At 
the bottom of the table are shown the quantities of acid used to 
obtain the acid color in each case. The use of acid phosphate in- 
stead of hydrochloric acid in two cases is because the stronger 
acid might . transform the indicator into that red form which 
occurs with all the sulfon phthalein indicators at very high acidi- 
ties. The 0.05 M HC1 is prepared with sufficient accuracy by 
diluting 1 cc. concentrated hydrochloric acid (specific gravity 1.19) 
to 240 cc. 



130 



THE DETERMINATION OF HYDROGEN IONS 



The alkaline form of the indicator is obtained in each case 
with a drop of alkali (two drops in the case of thymol blue). 
The alkali solution used for this purpose may be prepared 
with sufficient accuracy by making up a 0.2 per cent solution 
with ordinary stick NaOH. The indicator solutions may be 
made up as described on page 81 . Gillespie prefers the alcoholic 
solution in the case of methyl red and specifies it for soil work. 

TABLE 35 
Gillespie's table of pH values corresponding to various drop-ratios 



DROP-RATIO 


BROM- 

PHBNOL 
BLUE 


METHYL 
RED 


BROM- 
CRESOL 
PURPLE 


BROM-- 

THYMOL 

BLUE 


PHENOL 
RED 


CRESOL RED 


THYMOL 
BLUE 


1:9 


3.1 


4.05' 


5.3 


6.15 


6.75 


7.15 


7.85 


1.5:8.5 


3.3 


4.25 


5.5 


6.35 


6.95 


7.35 


8.05 


2:8 


3.5 


4.4 


5.7 


6.5 


7.1 


7.5 


8.2 


3:7 


3.7 


4.6 


5.9 


6.7 


7.3 


7.7 


8.4 


4:6 


3.9 


4.8 


6.1 


6.9 


7.5 


7.9 


8.6 


5:5 


4.1 


5.0 


6.3 


7.1 


7.7 


8.1 


8.8 


6:4 


4.3 


5.2 


6.5 


7.3 


7 9 


8.3 


9.0 


7:3 


4.5 


5.4 


6.7 


7.5 


8.1 


8.5 


9.2 


8:2 


4.7 


5.6 


6.9 


7.7 


8.3 


8.7 


9.4 


8.5:1.5 


4.8 


5.75 


7.0 


7.85 


8.45 


8.85 


9.55 


9:1 


5.0 


5.95 


7.2 


8.05 


8.65 


9.05 


9.75 


Produce 
acid color < 
with 


1 cc. of 

0.05m 

HC1 


1 drop 

of 

0.05m 

HC1 


1 drop 

of 

0.05m 

HC1 


1 drop 

of 

0.05m 

HC1 


1 drop 

of 
0.05m 
HC1 


1 drop of 

2 per cent 
H 2 KP0 4 


1 drop of 

2 per cent 
H2KPO4 



Gillespie proceeds as follows: 

Test tubes 1.5 cm. external diameter and 15 cm. long are suitable for 
the comparator and for the strengths given for the indicator solutions. It 
is advisable to select from a stock of tubes a sufficient number of uniform 
tubes by running into each 10 cc. water and retaining those which are filled 
nearly to the same height. A variation of 3 to 4 mm. in a height of 8 cm. 
is permissible. Test tubes without flanges are preferable. The tubes may 
be held together in pairs by means of one rubber band per pair, which is 
wound about the tubes in the form of two figure 8's. 

It is convenient to use metal test tube racks, one for each indicator, 
each rack holding two rows of tubes, accommodating one tube of each pair 
in front and one in back. For any desired indicator a set of color standards 
is prepared by placing from 1 to 9 drops of the indicator solution in the 9 
front tubes of the pairs and from 9 to 1 drops in the back row of tubes. A 



APPROXIMATE INDICATOR METHODS 131 

drop of alkali is then added to each of the tubes in the front row (2 drops in 
the case of thymol blue), sufficient to develop the full alkaline color and 
a quantity of acid is added to each of the tubes in the back row to develop 
the full acid color without causing a secondary change of color (see table 

35 for quantities) The volume is at once made up in all 

the tubes to a constant height (within about one drop) with distilled water, 
the height corresponding to 5 cc. 

These pairs are used in the comparator and matched with the 
tested solution. This tested solution is added to ten drops of the 
proper indicator until a volume of 5 cc. is attained and the tube 
is then placed in the comparator backed by a water blank. 

Gillespie describes the use of the comparator (page 70) and a 
modification for the accommodation of sets of three tubes used 
when colored solutions have to be compared. He also discusses 
a number of minor points and cautions against the indiscriminate 
comparison of measurements taken at different temperatures. 
For the details the original papers should be consulted. Were 
it not that the writer has seen evidence that the method has been 
applied with neglect of volume or concentration relations called 
for by the theory involved and carefully specified by Gillespie, 
it would seem unnecessary to advise that the principles be under- 
stood before the method is used. Certain other misconceptions 
of theory and practice found in a treatment of the method by 
Medalia (1920) have been corrected by Gillespie (1921). 

A very judicious appraisal of the method's value was given by 
Gillespie in these words: 

The method should be of especial use in orienting experiments, or in 
occasional experiments involving hydrogen ion exponent measurements, 
either where it is unnecessary to push to the highest degree of precision 
obtainable, or where the investigator may be content to carry out his 
measurements to his limit of precision and to record his results in such a 
form that they may be more closely interpreted when a more precise study 
of indicators shall have been completed. 

For the elaboration of certain manipulative details see Van 
Alstine (1920). 

If an indicator has only one color, for instance if it is yellow 
in the alkaline form and colorless in the acid form, it is evident 
that the method employed by Gillespie may be used with the 
slimination of one of the sets of tubes. Thus if 10 cc. of a tested 



132 



THE DETERMINATION OF HYDROGEN IONS 



solution containing 1 cc. of para nitro phenol matches 10 cc. of 
an alkaline solution containing 0.2 cc. of the same solution of 
the same indicator, it is known that the tested solution has in- 
duced a 20 per cent transformation of the indicator. Then a 
is 0.2. If now K IA has been determined, and if it has been shown 
that the simple dissociation formula holds for the indicator in 
use, equation 10 may be solved for pH. 

This procedure has been developed by Michaelis and co- 
workers; Biochem. Z. (1920) 109, 165; Biochem. Z. (1921) 119, 
307; Deut. med. Wochenschr. (1920) 46, 1238; 47, 465, 673; 
Z. Nahr. Genussm. (1921) 42, 75; Z. Immunitatsf. (1921) 32, 
194; Wochenschrift Brau. (1921) 38, 107. Calculations are 

ot 

aided by the use of a table relating a to log - . Such a 

1 — a 

table, somewhat more elaborate than that required for this special 
purpose, will be found on page 460 of the appendix. 

It is obviously necessary that K IA shall have been determined 
or that the actual experimental data relating the degree of color 
transformation to pH along the "dissociation curve" shall have 
been obtained. This necessary, fundamental "calibration" 
has been worked out by Michaelis and Gyemant (1920) and 
Michaelis and Kriiger (1921) (using hydrogen electrode measure- 
ments as a basis) for a series of one-color indicators. In the fol- 
lowing table are the pH values of the half -transformation points 
of the indicators used by Michaelis and Gyemant. These points 

correspond to log =r~ (see p. 26). 

-"■TA 



TABLE 36 
pH values of the half-transformation points of indicators. After Michaelis 



2, 6 dinitro phenol. . . 
2, 4 dinitro phenol. . . 

p-nitro phenol 

m-nitro phenol 

Phenolphthalein 

Alizarine Yellow GG 





TEMPERATURE 


10° 


20° 


30° 


40° 


3.74 


3.68 


3.62 


3.56 


4.11 


4.05 


3.99 


3.93 


7.27 


7.16 


7.04 


6.93 


8.43 


8.32 


8.21 


8.09 


9.82 


9.70 


9.58 


9.46 


11.26 


11.13 


11.00 


10.87 



50° 



3.51 
3.85 
6.81 
7.99 
9.34 
10.74 



APPROXIMATE INDICATOR METHODS 



133 



Now phenolphthalein, as we have already mentioned, is poly- 
acidic with dissociation constants so close to one another that 
the simple equation of a mono acid cannot be used. Alizarine 
Yellow GG suffers the same disadvantage. Consequently it is 
necessary in these cases to abandon the simple equation and the 
dissociation constants given above and to tabulate the experi- 
mental data. Michaelis and Gyemant have given the following 
tabulations. 

TABLE 37 
Degree of color, a, shown by phenolphthalein at indicated pH values. 
Temperature 18°C. 



a 


pH 


a 


pH 


(X 


pH 


0.01 


8.45 


0.16 


9.10 


0.55 


9.80 


0.014 


8.50 


0.21 


9.20 


0.60 


9.90 


0.030 


8.60 


0.27 


9.30 


0.65 


10.00 


0.047 


8.70 


0.34 


9.40 


0.70 


10.10 


0.069 


8.80 


0.40 


9.50 


0.75 


10.20 


0.090 


8.90 


0.45 


9.60 


0.80 


10.30 


0.120 


9.00 


0.50 


9.70 


0.845 
0.873 


10.40 
10.50 



TABLE 38 
Degree of color, a, shown by alizarine yellow GG at indicated pH values. 

Temperature 20°C. 



a 


PH 


a 


pH 


0.13 


10.00 


0.56 


11.20 


0.16 


10.20 


0.66 


11.40 


0.22 


10.40 


0.75 


11.60 


0.29 


10.60 


0.83 


11.80 


0.36 


10.80 


0.88 


12.00 


0.46 


11.00 







For 2, 5-dinitrophenol log 



K, 



is 5.15 for solutions of very 



low salt concentrations, 5.08 for solutions of 0.15 M salt concen- 
tration and 5.02 for solutions of 0.5 M salt concentration. 

For 3, 4-dinitro phenol log ~zz~ is about 5.3 and for 2, 3-dini- 

-"■IA 

trophenol about 4.8. 



134 THE DETERMINATION OF HYDROGEN IONS 

With these data we are now prepared to measure pH values 
without the use of standard buffer solutions. 
The following indicator solutions are used: 

1. 2, 4 dinitro phenol (a dinitro phenol) 0.05 per cent aqueous solution 

2. 2, 6 dinitro phenol (/3 dinitro phenol) saturated aqueous solution 

formed at high temperature and filtered from crystals. 

3. 2, 5 dinitro phenol (y dinitro phenol) 0.025 per cent- aqueous 

solution. 

4. 3, 4 dinitro phenol (5 dinitro phenol) concentration not given. 

5. 2, 3 dinitro phenol (e dinitro phenol) concentration not given. 

6. p-nitro phenol 0.1 per cent aqueous solution. 

7. m-nitro phenol 0.3 per cent aqueous solution. 

8. phenol phthalein 0.04 per cent solution in 30 per cent alcohol. 

9. Alizarine yellow GG (salicyl yellow, m-nitrobenzene azo salicylic 

acid) saturated alcoholic solution diluted to convenient strength. 

Test tubes must be of equal bore. A measured amount of the 
solution to be tested (e.g. 10 cc.) is mixed with the proper indicator 
in such amount that a rather weak color is developed. To a 
second test tube containing 9 cc. N/100 NaOH there is added 
such a volume of the indicator solution that the color developed 
approximately matches that of the first tube. The volume of 
the second tube is now made up to the volume of the first. If the 
two tubes do not match in color, another trial is made with more 
or less indicator until a color match is obtained. The amount 
of fully transformed indicator in the second tube then corresponds 
to that amount of indicator in the first tube which has been trans- 
formed to the colored tautomer. Let us assume that 1.0 cc. 
was added to the tested solution and that a color match occurs 
when 0.1 cc. of the same indicator solution was placed in the second 
alkaline tube and made up to the volume of the first. Then the 
percentage color transformation induced by the tested solution 

was 10. 

a 

Hence a = 0.1 and log = — 0.95. 

1 — a 

If the indicator used was p-nitrophenol and the temperature 
was 20°C. pH = 7.16 - .95 = 6.21 (6.2) 

If the indicator was phenolphthalein table 37 shows that the 
pH was about 9.0. 

For routine work in the range pH 2.8 to 8.4 Michaelis (1921) 
recommends the following system. 



APPROXIMATE INDICATOR METHODS 



135 



To uniform test tubes are added seriatim the volumes of indica- 
tor solution given in the following tables, the indicator solution 
being prepared by diluting the stock solutions (page 134) ten times 
with 0.1 normal soda solution (sic). Each tube is now filled to a 
7 cc. mark with the soda (sic) solution. (In the original paper 
Michaelis and Gyemant describe dilutions with N/100 NaOH 
solution.) 

TABLE 39 

m-nitro phenol 



Tube number 

Cubic centimeters of indicator. 
pH 



1 
5.2 

8.4 



2 

4.2 
8.2 



3 
3.0 

8.0 



4 
2.3 

7.8 



5 
1.5 
7.6 



6 
1.0 
7.4 



7 
0.66 
7.2 



0.43 
7.0 



9 
0.27 
6.8 



p-nitro phenol 



Tube number 

Cubic centimeters of indicator. . 
pH 



10 


11 


12 


13 


14 


15 


16 


17 


4.05 


3.0 


2.0 


1.4 


0.94 


0.63 


0.4 


0.25 


7.0 


6.8 


6.6 


6.4 


6.2 


6.0 


5.8 


5.6 



18 
0.16 
5.4 



#, 5-dinitro phenol (y dinitro phenol) 



Tube number 


19 
6.6 

5.4 


20 
5.5 
5.2 


21 
4.5 
5.0 


22 
3.4 

4.8 


23 
2.4 
4.6 


24 
1.65 
4.4 


25 
1.1 

4.2 


26 


pH 


0.74 
4 







2, 4-dinitro phenol (a dinitro phenol) 



Tube number 

Cubic centimeters of indicator. 
pH 



27 


28 


29 


30 


31 


32 


33 


34 


6.7 


5.7 


4.6 


3.4 


2.5 


1.74 


1.20 


0.78 


4.4 


4.2 


4.0 


3.8 


3.6 


3.4 


3.2 


3.0 



35 
0.51 

2.8 



The test tubes are sealed with paraffined corks and when not 
in use are protected from the light. 

To test a solution for its pH value 6 cc. are taken and 1 cc. 
indicator solution added. The solution is then compared with 
the standards. 

For testing the pH values of waters Michaelis (1921) operates 
as follows: 

A stock solution containing 0.3 gram pure m-nitro phenol in 
300 cc. distilled water is diluted before use by adding to 1 cc. 
of the stock 9 cc. distilled water. There are used flat bottom 
tubes of about 25 cm. height and 14 mm. internal diameter having 
such uniformity that 40 cc. of water will stand at a height of 



136 THE DETERMINATION OF HYDROGEN IONS 

between 22 and 23 cm. To six such tubes are added seriatim 
0.25; 0.29; 0.33; 0.38; 0.45 and 0.50 cc. of the diluted m-nitro 
phenol solution. To each tube are added 40 cc. of an approximately 
N/50 NaOH solution freshly prepared by dilution of an approxi- 
mately normal solution. These are the standards. 

To test a water, 40 cc. are added to a tube of correct dimensions 
and to this is added sufficient indicator to develop a. color within 
the range of the standards, preferably near the brighter of the 
standards. Comparison is now made as in Nesslerization, after 
having waited two minutes for completion of the mixing. 

The amount of indicator in the alkaline, matching standard 
corresponds to the amount transformed to the colored form by 
the tested solution. Therefore, the cubic centimeters of indica- 
tor in the standard divided by the cubic centimeters in the tested 
solution is a, the degree of color transformation, or when multi- 
plied by 100 the percentage color transformation. 

Michaelis and his co-workers have tabulated corrections for 
temperature and for salt concentrations. The operator should 
determine for himself not only the order of accuracy required in 
his problem but his own ability to make readings with that pre- 
cision which will make corrections significant. He may then 
refer to the original papers for tables giving corrections for salt 
effects and for temperature. The order of magnitude of these 
corrections may be seen in the following example. 

For m-nitrophenol Michaelis and Kriiger give the following 

values of log zz~ at 17°C. in solutions of the indicated salt 
concentrations. 

TABLE 40 



MOLECULAR 8ALT CONTENT 


K AI 


O-0.01 


8.33 


0.05 


8.28 


0.10 i 


8.23 


0.15 


8.22 


0.20 


8.18 


0.3-0.6 


8.17 


to 1.0 


8.15 



APPROXIMATE INDICATOR METHODS 



137 



The temperature corrections to be added when m-nitrophenol 
is used at temperatures other than 17.5°C. are as follows. 



TABLE 41 



t° 


CORRECTION 


t° 


CORRECTION 


5 


+0.10 


25 


-0.06 


10 


+0.06 


30 


-0.11 


15 


+0.02 


35 


-0.15 


17.5 


±0.00 


40 


-0.18 


20 


-0.02 


45 


-0.22 






50 


-0.26 



In spite of the fact that the nitro compounds used by Micha- 
elis and Gyemant are of wan color and those tried in the survey 
made by Clark and Lubs were neglected for this reason, Micha- 
elis and Gyemant describe the application of their method to 
colored solutions. 

Advantage is taken of the fact that many solutions are inappre- 
ciably altered in pH by diluting five or even ten times (see page 
37). For dilution, Michaelis and Gyemant use freshly boiled 
NaCl solution of a concentration approximately that of the test 
solution. If on dilution the natural color still interferes with 
the use of an indicator, the natural color may be duplicated in 
the standard by the use of supplementary dyes such as S0rensen 
uses. Or, if addition of alkali does not alter the natural color of 
the solution under test, the, standard may be made up with an 
alkaline solution of the tested solution itself. In this case it is 
necessary to be on guard against the buffer action and to add 
alkali until no increase in the color of the indicator is observed. 

Without doubt the preferable procedure to follow when apply- 
ing the Michaelis and Gyemant method or any other method to 
colored solutions is to use the "comparator" described on page 
70 and illustrated in figure 8. 

The method of Michaelis and Gyemant is fundamentally the 
same as that of Gillespie and should, therefore, be used with the 
qualifications which Gillespie has stated. There is a distinct 
advantage in the use of the nitro phenols for they have been found 
to have relatively small protein and salt errors. It is sometimes 
accessary to use very high concentrations of the indicator, and 



138 THE DETERMINATION OF HYDROGEN IONS 

in such circumstances one must be on guard against the effect of 
the indicator itself or of impurities. 

Indicator paper. Although a favorite form of indicator is the 
deposit on a strip of paper (for example the familiar litmus paper) 
it is to be avoided unless the use of an indicator solution is pre- 
cluded. It is to be avoided because the factors involved in the 
reaction between solution and indicator are made complex by 
the capillary action of the paper or the material entrained in 
these capillaries. On the other hand there are occasions when 
an approximate measure of pH is sufficient and when an indicator- 
paper is to be preferred. On such an occasion it is desirable to 
know the difficulties to be encountered. We are indebted to 
Walpole (1913) and others but particularly to Kolthoff (1919, 
1921) for investigations on this subject. Kolthoff has given 
particular attention to the sensitivity of indicator papers when 
used in titrations, a situation where there is generally but little 
buffer action near the end-point. Under such circumstances 
there are to be regarded a number of details which are described 
at length in Kolthoff' s papers. Several of these details will be 
perceived if we describe some of the more important aspects of 
the indicator-paper method of determining pH. 

In general one must ride either horn of the following dilemma. 
The paper is sized, in which case the buffer action of the tested 
solution must be strong enough and allowed time enough to over- 
come the buffer action of the sizing. Or the paper has the quali- 
ties of filter paper, in which case the solution tested will spread 
and leave rings of different composition formed by the adsorp- 
tive power of the capillaries. 

Kolthoff found that various treatments and selections of filter 
paper are of secondary importance, so the choice lies between 
sized and unsized paper. Now certain coloring matters are ad- 
sorbed by filter paper so that a separation is possible and the 
clear solution can be found in a ring about the point of contact 
between a tested colored solution and the indicator paper. But 
beyond this ring is a much more dilute one and unless one knows 
the properties of the system under examination it is not easy to 
correctly estimate the pH of the solution from the appearances 
of the paper. 

Although coated paper may lose in sensitivity by not taking 



APPROXIMATE INDICATOR METHODS 139 

up so much indicator as filter paper and must be used with strongly 
buffered solutions it is the more convenient. In any case the 
paper should be left in contact with the tested solution a generous 
length of time, for the establishment of equilibrium may be very 
slow (Walpole), and there must be instinctively exercised a men- 
tal plotting of the time curve. 

If, after having exhausted all other methods, it is found that 
the indicator-paper method is the better adapted to a particular 
set of circumstances, the procedure should be calibrated to the 
purpose at hand rather than forced to render accurate pH values. 

Dilution. As indicated in Chapter II a well buffered solution 
may often be moderately diluted without seriously altering the 
pH. 

When dealing with complex solutions which are mixtures of 
very weakly dissociated acids and bases in the presence of their 
salts, and especially when the solution is already near neutrality 
dilution has a very small effect on pH, so that if we are using the 
crude colorimetric method of determining pH a five-fold dilution 
of the solution to be tested will not affect the result through the 
small change in the actual hydrogen ion concentration. Differ- 
ences which may be observed are quite likely to be due to change 
in the protein or salt content. For this reason as well as for other 
reasons Glark and Lubs (1917) considered it wise to use M/20 
standard comparison solutions instead of more concentrated stand- 
ards for bacteriological media where dilution is often advantageous. 
The salt content of the standards undoubtedly influences the 
indicators and should be made as comparable as is convenient 
with the salt content of the solutions tested when these are diluted 
to obtain a better view of the indicator color. 

The conclusion that dilution has little effect on the hydrogen 
ion concentrations of many solutions has long been recognized. 
Michaelis (1914) found little change in the pH of blood upon 
dilution, and Levy, Rowntree, and Marriott (1915) depended 
upon this in part in their dialysis method for the colorimetric 
determination of the hydrogen ion concentration of blood. Hen- 
derson and Palmer (1913) have used the dilution method in de- 
termining the pH of urines, and Paul (1914) records some experi- 
ments with wines the pH values of which were affected but little 
by dilution. The legitimacy of dilution has been tacitly admitted 



140 THE DETERMINATION OF HYDROGEN IONS 

by bacteriologists in their procedure of diluting media to be 
titrated to what is in reality a given pH as indicated by 
phenolphthalein. 

In the examination of soil extracts colorimetrically little could 
be done were the "soil-solution" not diluted. Whatever may be 
the effect it is certain that the correlations between the pH values 
of such extracts and soil conditions is proving of great value (see 
Chapter XXI). Wherry has developed a field kit of the sulfon 
phthalein indicators with which he has found some remarkable 
correlations between plant distribution and the pH of the native 
soils. This field kit is now on the market. 

The use of indicators in bacteriology. Perhaps no other science 
requires such continuous routine use of indicators as does bac- 
teriology. This use is chiefly in the adjustment of the reaction 
of culture media and in the testing of the direction and limits of 
fermentation. While these are but examples, the frequency with 
which they become matters of routine warrant a brief outline of 
special procedures. 

If experience has shown that the pH of the medium may lie 
within a zone about 0.5 units of pH wide, it is sufficient to add 
unstandardized acid or alkali, as the case may be, until a portion 
of the medium tested with the proper indicator in proper concen- 
tration approximately matches that color standard shown in the 
color chart of page 50 corresponding to the pH value to be ap- 
proximated. This requires experience in overcoming the confusing 
effect of the natural color of the medium and also a well established 
sense of color memory. The beginner should proceed in some 
such way as the following. 

It is desired, for instance, to adjust a colorless medium to pH 
7.5. The medium as prepared is somewhat below the final vol- 
ume. A quick, rough test at room temperature shows that the 
pH value lies between 6.0 and 6.5. Therefore, alkali must be 
added. The 'alkali solution to be used need not be standardized 
but may be about 1 normal. An exact one-in-ten dilution of 
this is run into 5 cc. of the medium to which has been added 5 
drops of phenol red solution. Titration is continued until the 
color nearly matches 10 cc. of standard buffer "7.5." The tube 
of medium is now diluted to 10 cc. so that a color comparison 
may be made between test solution and standard, each contain- 



APPROXIMATE INDICATOR METHODS 141 

s 

ing the same concentration of indicator. The tubes are viewed 
through equal depths of solution. If the desired point 7.5 has 
been overstepped another trial is made. If 7.5 is not reached a 
moderate addition of alkali may be made without serious viola- 
tion of volume requirements, and a second reading is taken. 

Having made estimates of the pH values in the two readings 
an interpolation is made of the amount of dilute alkali required 
to bring the medium to exactly pH 7.5. From this is calculated 
the amount of the stronger alkali required for the main batch. 
Having added this a check determination is made. When 
finally adjusted the medium is diluted to its final volume. Most 
culture media suffer alterations of their pH values during sterili- 
zation and consequently allowance must be made if the final 
pH value is to be exact. This allowance will vary with the medium 
but can easily be determined for a standard medium prepared 
under uniform conditions. 

When the color or turbidity of a tested solution interferes with 
direct color comparisons proceed as above but make comparisons 
by means of the Walpole compensation method described on 
page 70. 

It need hardly be said that if the requirements of an organism 
are such that the desired pH value cannot be obtained with phenol 
red a more suitable indicator is selected from table 6 and if the 
medium requires the addition of acid an unstandardized acid 
solution approximately normal (or stronger) and an exact 1:10 
dilution of this are substituted for the alkali solutions mentioned 
above. 

In testing fermentations it often happens that the final hydro*- 
gen ion concentration is of more significance than the amount of 
acid or alkali formed; but the two distinct types of data are not 
to be confused to the complete displacement of either. It is 
sometimes convenient to incorporate the indicator with the 
medium provided the indicator is not reduced or destroyed by 
the bacterial action. The sulfon phthaleins are particularly use- 
ful for they are not reduced except by the more active anaerobes. 
Brom cresol purple replaces litmus in the common milk-fermenta- 
tion tests without introducing that confusion which the reduction 
of litmus causes. It reveals differences in pH even beyond the 
range of its usefulness for ordinary measurements, passing from a 



142 THE DETERMINATION OF HYDROGEN IONS 

greyish blue in normal milk to more and more brilliant yellows 
with the development of acidity, and to a deep blue with the 
development of alkalinity. For further details see Clark and 
Lubs (1917). 

In the method of Clark and Lubs (1915, 1916) for the differenti- 
ation of the two main groups of the coli-aerogenes bacteria, as 
well as in the similar method of Avery and Cullen (1919) for 
separating streptococci, the composition of the medium is so 
adjusted to the metabolic powers of the organisms, that the 
reaction is left acid to methyl red in one case, and alkaline in 
the other. No exact pH measurements are necessary. In cases 
where large numbers of cultures falling within the range of one 
indicator are to be tested, the cultures may be treated with the 
indicator and compared by grouping. A careful determination 
made upon one member of a homogeneous group will serve for all. 
In this way large numbers of cultures may be tested in a day. 

Special uses. While on the subject of approximate determina- 
tions with indicators a word may be said about the usefulness of 
the quick, rough test. 

Almost every investigator has come to realize that among the 
mistakes in labeling chemicals the more frequent are cases in 
which a basic salt is labeled as an acid salt and vice versa. Now 
a solution of NajjHPC^, for example, has a pH value, which, 
while easily displaced (see figure 5), distinguishes it definitely 
from a solution of NaH 2 P0 4 or Na 3 P0 4 . Indeed some idea may 
be obtained of the degree of impurity if the pH value of a dilute 
solution is displaced definitely from about pH 8.5. Some serious 
accidents are said to have occurred in medical practice by the 
use of sodium citrate purported to be neutral and too late found 
to be acidic. One short, swift test with an indicator could have 
revealed the situation, and averted the accident. 

Indeed there are a great many substances solutions of which 
have either a buffered and definite pH value, as in the case of 
acid potassium phthalate, or else a pH value easily displaced 
by impurities from that of the absolutely pure substance but 
still falling within limits, as in the case of the primary and second- 
ary phosphates. When properly defined, such values can be 
made part of the specifications for purity. Especially in the 
case of drugs which are often used beyond the reach of the assay 



APPROXIMATE INDICATOR METHODS 143 

laboratory a simple indicator test should prove helpful as sug- 
gested by Evers (1921) and especially emphasized by Kolthoff 
(1921). 

In the case of milk it is quite impossible to define the pH by a 
comparison of the color of an indicator in the milk with the 
color of the indicator in a clear standard; yet differences are made 
distinctly evident, and, if taken only for what they actually 
mean, are helpful in the grading of milk and in the study of the 
conduct of different bacteria inoculated into sterile milk. Clark 
and Lubs (1917) called attention to the superiority of the sul- 
fonphthalein indicators, especially brom cresol purple, for this 
purpose. 

Spotting. When only small quantities of solution are available or 
when highly colored solutions are to be roughly measured, their ex- 
amination in drops against a brilliant white background of "opal" 
glass is often helpful. In the examination of colorless solutions 
comparisons with standards may be made as follows. A drop of 
the solution under examination is mixed with a drop of the proper 
indicator solution upon a piece of opal glass. About this are 
placed drops of standard solutions and with each is mixed a 
drop of the indicator solution used with the solution under 
examination. Direct comparison is then made. Felton who 
developed details in this method for the examination of small 
quantities of solutions used in tissue-culture investigations found 
mixtures of indicators of particular value for orientation. Equal 
parts of methyl red and brom thymol blue, for instance, give 
brilliant color contrasts in this drop method between about pH 
4.6 and 7.6; but with an unsatisfactory zone between 5.6 and 6.2. 
Methyl red and brom cresol purple are used between pH 4.6 
and 7 while for rough work between 1.2 and 9 methyl red and 
thymol blue are used. These mixtures are used only as "feel- 
ers." The opal glass or porcelain upon which the tests are to be 
made should be carefully tested for the absence of material 
seriously affecting the acid-base equilibria of the material under 
examination. Errors due to unequal drops, evaporation and 
impurity of indicator are to be watched for. For further details 
see Felton (1921). 



CHAPTER IX 

Outline of the Electrometric Method 

A noble metal coated with platinum black, which will hold large 
quantities of hydrogen, may be made to serve as a hydrogen elec- 
trode. When it is laden with hydrogen and immersed in a solution 
containing hydrogen ions, there is exhibited a difference of elec- 
trical potential between solution and electrode which is depend- 
ent upon the concentration of the hydrogen ions; just as the 
potential difference between a silver electrode and a solution of 
silver ions is dependent upon the concentration of the silver ions. 

We have no reliable means of measuring this single potential 
difference; but when we join two hydrogen electrodes, as shown 
in figure 13, we can not only measure the difference between the 
aforementioned differences of potential, i.e., the total electro- 
motive force (E. M. F.) of the "gas chain" as it is called, but we 
can also derive an equation showing how this E. M. F. will vary 
with the ratio of the concentrations of the hydrogen ions about 
the two electrodes. If C is the concentration of the hydrogen ions 
in one solution and C the concentration in the other, the E. M. F. 
of the combination will be related to the ratio of the concentrations 
by the following equation expressed in numerical form for a 
temperature of 25°C. 

E. M. F. = 0.059 log §- 
C 

We shall leave to the next chapter the derivation of the equa- 
tion and shall now put it in a form not restricted to the particular 
temperature of 25°C. assumed above. 

C 
E. M. F. = 0.000,198,37 T log ~; 

Here T is the absolute temperature, the zero point of which is 
273.09° below 0°C. A table giving the values of 0.000,198,37 T 
for various temperatures centigrade is given in the Appendix. 
Thus if we join two hydrogen electrodes as illustrated in figure 
13 measurements of the electromotive force of the chain and of 

144 



OUTLINE OF ELECTROMETRIC METHOD 



145 



the temperature allow us to calculate the ratio of the one hydro- 
gen ion concentration to the other. Then if one hydrogen ion 
concentration is known we may derive the other. 

As the "known" there may be used any one of the buffer solu- 
tions described in Chapter VI. The reader should note, however, 
that the values of these "known" solutions are derived from 



H, 



i 




[1 



no 



n 



I 



e:->-3£ 



- - - -o- 




I 

n' t ". ' . * 

SSL, 



ihsos 



= -=ur=^o^ 




Fig. 13. Diagram op Concentration Chain of Hydrogen Electrodes 

hydrogen electrode measurements which, as we have just seen, 
furnish ratios only. Some ultimate standard is therefore implied. 
This is discussed in Chapter XIX. 

If there be no means at hand for measuring the electromotive 
force but there is available a galvanometer or a home-made capil- 
lary electrometer for detecting small currents, the following 
procedure may be used. Two hydrogen electrodes are set up as 
in figure 13. By means of the buffer solutions described in Chap- 
ter VI the hydrogen ion concentration in one electrode vessel is 
varied until no difference of potential occurs between the two 
electrodes. This point is determined by absence of deflection 



i 



146 THE DETERMINATION OF HYDROGEN IONS 

in the galvanometer or by no change in the meniscus of the capil- 
lary electrometer. Then C = C in the above equation. 

Instead of setting up two hydrogen electrodes, one of which 
is a known standard, it is generally more convenient to replace 
the standard hydrogen electrode by a more permanent "half 
cell" such as the "calomel electrode." This is an electrode of 
mercury covered with calomel in the presence of a definite KC1 
solution, for example saturated KC1 solution. If this so-called 
"saturated calomel electrode" is used, a tube containing sat- 
urated KC1 is led directly to the solution in the hydrogen electrode 
vessel. 

Now suppose that in the first place there were used two hydro- 
gen electrodes as in figure 13, and let it be assumed that one of 
these was immersed in a solution normal with respect to hydro- 
gen ions. Let C be identified as 1 normal and C, the unknown 

1 
be less than 1 normal. Then E. M. F. = 0.000,198,37 T log 7J 

Now suppose that the normal hydrogen electrode is connected 
with a "saturated calomel electrode." We might then have 
an arrangement as follows: 

(saturated calomel electrode 



II 
III 



►normal hydrogen electrode 
(hydrogen electrode in [H + ] = C' 



I 



Suppose the difference II has already been determined and 
that I is measured in the immediate experiment. Then I — 
II = III. Having found III, we can use the equation for two 
hydrogen electrodes, one of which is the "normal," and so solve 
directly for C 

At 25°C. the mercury of the calomel electrode is 0.246 volt 
more positive than the platinum of the normal hydrogen elec- 
trode. 

Hence: observed E. M. F. - 0.246 = III 

I - II = III 

III = 0.000,198,37 T log pp. 

At 25°C, T = 273.09 + 25 = 298.09. 



OUTLINE OF ELECTROMETRIC METHOD 147 

Then observed E. M. F. - 0.246 = 0.0591 log —,. 

But log — ; = pH. 

Observed E.M.F. - 0.246 „ 

= pH. 

0.0591 F 

If the observed E. M. F. is 0.648, pH = 6.80. 

Although it is impracticable to describe at this point the details 
of a complete system for the measurement of hydrogen ion con- 
centration an outline may be given with which to coordinate 
the main features as they will develop in subsequent chapters. 

Figure 14 illustrates a simple system which may be put together 
from inexpensive material. It is not a system which can be 
recommended for precise or even routine measurements, but it 
will work and is well adapted to show the principles concerned. 

Hydrogen, prepared by one of the methods described in Chap- 
ter XV, passes into the hydrogen electrode vessel A and escapes • 
at B. Connected with this vessel by the siphon S, filled with a 
saturated KC1 solution, is the calomel electrode M consisting of a 
layer of mercury covered by calomel under a saturated solution 
of KC1. The hydrogen electrode H consists of a piece of plati- 
num foil covered with platinum black. It is welded to a plati- 
num wire which is sealed into the glass tube. 

Hydrogen is bubbled through the solution in A until solution 
and electrode are thoroughly saturated with the gas. 

The difference between the potential difference at the mercury- 
calomel junction and the potential difference at the hydrogen 
3lectrode-solution junction is now measured by means of a po- 
tentiometer. A simple form of this is illustrated. 

A storage battery P sends current through the rheostat R, the 
calibrated resistance-wire K-L and the fixed resistance L-F. By 
properly setting the switch O a Weston cell W having an electro- 
notive force of 1.018 volts can be connected to K and F, the 
f pole of the Weston cell being connected to the + side of the 
>attery current. The rheostat R is now varied until there is 
io deflection of the galvanometer or electrometer E. Then the 
i lifference of potential between K and F is equal to the E. M. F. 
t f the Weston cell. The resistance K-L is such that when the 






148 THE DETERMINATION OF HYDROGEN IONS 

above adjustment is made the difference of potential between 
K and L is one volt. A scale properly divided is placed beside 
the wire K-L. When the sliding contact X is at K there will be 
no difference of potential between X and K. When X is at L 
the difference of potential between X and K will be one volt. 
When X is at some intermediate position the difference of potential 
between X and K will be that fraction of one volt indicated by 
the scale. 

Having first carefully adjusted the potentiometer by means 
of the standard Weston cell the switch O is thrown to connect 
the calomel electrode-hydrogen electrode system and X is slid 
in one direction or the other until the galvanometer E shows no 
deflection. Then the difference of potential between X and 
K is equal to the difference of potential between mercury and 
platinum. 

The temperature is read and the data put into the equations 
given above. 

Neither measured E. M. F. nor Weston cell should be left in 
circuit for more than an instant. While switch can be used 
for this momentary completion of circuit, it is more convenient 
to use a telegraph key in the galvanometer circuit. 

If care be taken to maintain the hydrogen at barometric pres- 
sure, the effects of minor variations of the barometer from sea 
level conditions and of displacement of hydrogen by water vapor 
may be neglected in rough measurements. A discussion of the 
barometric pressure is found in the next chapter. 

In all cases where two unlike solutions are joined as in figure 
13, there will develop a local potential difference at the liquid 
junction. To deal with this precisely is the most difficult of the 
problems encountered. The subject is discussed in Chapter XI. 
In very many instances, however, the employment of a saturated 
solution of KC1 as is specified in the apparatus illustrated in 
figure 14, reduces the liquid junction potential difference to an 
order of magnitude which is negligible. 

Since variations may occur in the calomel electrode or in the 
reliability of the hydrogen electrode it is well to check the system 
frequently by means of measurements made with standard solu- 
tions. Some of these are described in Chapter XVIII. 

In the use of the potentiometer the elementary principles 
must be understood lest standard cells or half-cells be injured 



OUTLINE OF ELECTROMETRIC METHOD 



149 



or quite erroneous results obtained. Therefore, these principles 
are discussed in Chapter XIV. 




Fig. 14. A Simple Arrangement for Electrometric Measurement 

of pH. 

Were it not for the fact that several experimenters have tried 
to make hydrogen electrode measurements by use of conductivity 
nstruments, it would seem hardly necessary to say that the meas- 
lrement of conductivity or its reciprocal, resistance, is a proce- 
lure entirely different from the measurement of electromotive 
orces or potential differences. 1 

1 The surprising number of cases in which this confusion has been 
evealed may be an interesting psychological result of the emphasis hitherto 
)laced upon conductivity measurements, sometimes to the entire exclusion 
if any reference to potentiometric measurements. 



150 THE DETERMINATION OF HYDROGEN IONS 

If the beginner is puzzled by the array of apparatus described 
in the following pages he may welcome the following suggestion. 
The main outline of a problem can often be denned by the use 
of the Hildebrand electrode used in connection with the saturated 
calomel half-cell and by using as a potentiometer the voltmeter 
system. This set of apparatus is illustrated in figure 28. It not 
infrequently happens that the outlining of a problem with this or 
a comparable system will indicate that further refinement would 
be useless or confusing. It also frequently happens that the errors 
suggest phantom relations or obscure existing relations of im- 
portance. It is, therefore, advisable whenever possible to keep 
the accuracy of measurements just ahead of the immediate de- 
mands. To meet this requirement the investigator must gain 
the ability to judge for himself the apparatus required and it is 
to contribute toward this and the pleasure of work that the follow- 
ing chapters are written in some detail. If the reader does not 
care to work out the peculiar requirements of his problem he is 
advised, after having outlined his problem with the system men- 
tioned above, to obtain a reliable potentiometer of standard, 
not unique, design and to use the system illustrated in figure 19. 
In the first instance accurate temperature control is unnecessary. 
In the second instance it is advisable if for no other purpose than 
the avoidance of vexatious uncertainties. 



CHAPTER X 

Theory of the Hydrogen Electrode 

In treating the theory of the hydrogen electrode we shall first 
consider Nernst's (1889) conception of electrolytic solution tension 
as a useful way of remembering certain important relations and 
then pass to the thermodynamic derivation of the E. M. F. of 
a concentration cell. 

If a metal be placed in a solution of its salt there will be a differ- 
ence of electrical potential between metal and solution which will 
vary in an orderly manner with the concentration of the metal ions. 
To account for the difference of potential Nernst assumed that a 
metal possesses a characteristic solution tension comparable with 
the vapor pressure of a liquid, or, better, with the solution pres- 
sure of a crystal of sugar — but with the important qualification 
that it is the metal ions which pass into solution. Imagine first 
that the metal is in contact with pure water. The metal ions 
passing into solution carry their positive charges and leave the 
metal negative. Thus there is established a so-called double 
layer of electrical charges at the interface between metal and solu- 
tion, the solution being positively and the metal negatively 
charged relative to one another. This potential difference forcibly 
opposes further dissolution of metallic ions, for the relative posi- 
tive electrical field in the solution and the relative negative field 
in the metal restrain any further migration of positively charged 
Dodies from the metal to the solution. Equilibrium is established 
vhen the electrostatic control equalizes the solution pressure. 
If now there are already in the solution ions of the .metal, the 
•elative electrostatic field in the solution has already been par- 
ially established, fewer ions will escape from the metal and the 
netal is left more positive. 

Therefore the higher the concentration of the positive metallic 
ons in the solution the more positive will be the charge on the 
netal and, conversely, the lower the concentration of the metallic 
ons in the solution the more negative will be the charge on the 
aetal. 

151 



152 THE DETERMINATION OF HYDROGEN IONS 

Not only metals but various gases are found to act in a similar 
way when means are devised to bring them into a situation as 
easily handled as are metal electrodes. Hydrogen is one of these 
gases and the means of handling it as an electromotively active 
gas is to take it up in one of those metals such as platinum, pal- 
ladium or iridium which in a finely divided condition hold large 
quantities of hydrogen. Platinum black deposited upon plati- 
num and laden with hydrogen forms a hydrogen electrode. It 
can be brought into equilibrium with hydrogen ions as silver is 
brought into equilibrium with silver ions; and the more positive 
it becomes the higher must be the concentration of the positively 
charged hydrogen ions in the surrounding solution. 

It remains however to formulate with mathematical precision 
the way in which the potential of the hydrogen electrode changes 
with the concentration of the hydrogen ions; and for this purpose 
the energy relations must be considered. 

Suppose a metal electrode dips into a solution of ions of the 
same metal. Let the concentration of these ions be such that 
their partial pressure, which would be manifest in an arrangement 
for producing osmotic pressure, is P in the volume V. 

Let the electrode be of such a size that one gram mol of ions, 
carrying nF faraday of electricty, can pass from electrode to 
solution to there raise the partial pressure by dP. The increase of 
the difference of potential between electrode and solution will be 
dE. The electrical work expended will then be nFdE and the 
work taken up by the material system will be VdP. If the 
process is reversible, and the system is allowed to return to the 
original state, 

nFdE - VdP = 

VdP 
or dE = -^=-. (26) 

nF 

We shall now assume that we are dealing with an "ideal solu- 
tion" by which we mean a solution in which the pressure-volume 
relation of the ions conforms to the gas law for a "perfect gas," 

T>rp 

then PV=RT or V = -p . 



THEORY OF THE HYDROGEN ELECTRODE 153 

Substituting this equivalent of V in equation (26) we have 

dE = 5T dP 
nFP 

On integration this becomes 

E = — InP + K (27) 

nF 

where In is the symbol for natural logarithm to the base e and K 
is an integration constant. 

The integration constant is the point of reference for the gen- 

TJT 
eral relation E = — In P. It is the potential difference between 

nF 

electrode and solution when some arbitrary unit of pressure 
is chosen and P = 1. Then in accordance with the unit chosen 
E = K. 

LeBlanc (1907) and others have substituted for K an equiv- 

T»T 

alent constant of the form — In p, called p the electrolytic 

nF 

solution tension of Nernst and so obtained the relation 

E = In — 

nF p 

But it is of doubtful value to postulate the physical signifi- 
cance of K in this manner. For present purposes we can afford 
to leave K as it stands, a pure integration constant. 

Let us consider now the arrangement known as a concentration 
cell. Let the two vessels of figure 13 contain the same metal ion 
in concentrations C and C corresponding to "osmotic pressures" 
P and P'. Let there dip into each solution an electrode of the 
metal. Let the two solutions be connected by a siphon, and the 
slectrodes by a device for measuring the E. M. F. 

Using the equation (27) developed above we know that at elec- 

T?T 
;rode 1 there will be a difference of potential E = — In P + K and 

nF 
PT 
it electrode 2 a difference of potential E' = — In P' + K. The 

nF 



154 THE DETERMINATION OF HYDROGEN IONS 

total E. M. F. will be the algebraic sum of these potential dif- 
ferences. If P' be less than P, the electrode in contact with the 
ions at partial pressure P' will be negative to the electrode in 
contact with the ions at partial pressure P. Hence 

E.M.F. = E-E'= — lnP + K-T— lnP' + K~|= —In-- 
nF LnF J nF P' 

Since the ratio of the pressures may be considered equal to the 
ratio of the ion concentrations, 

E. M. F. = — In - (28) 

nF C 

This is the fundamental equation for the E. M. F. of a concen- 
tration chain. 

R is the gas constant, T the absolute temperature, (273.09+ 
t centigrade), n the valency of the ion and F the faraday or the 
quantity of electricity associated with 1 gram molecule equivalent. 

To put this equation into working form there have to be found 
the electrical equivalents for R and F. Since measurements of 
potential are to be made in terms of the international volt this and 
the related units will first be denned as they are given in Bureau 
of Standards Circular No. 60 (1916), "Electrical Units and 
Standards." 

International ohm. The international ohm, which is generally 
referred to as the ohm, but which is to be distinguished as are 
other international units from the " absolute" units, is denned as 
"the resistance offered to an unvarying electric current by a col- 
umn of mercury at the temperature of melting ice, 14.4521 grams 
in mass, of a constant cross-sectional area and of a length of 
106.300 cm." 

International ampere. The international ampere, generally re- 
ferred to as the ampere, is defined as "the unvarying electric cur- 
rent which, when passed through a solution of nitrate of silver 
in water in accordance with specification II (of the 1908 London 
Conference), deposits silver at the rate of 0.00111800 of a gram 
per second." 

International volt. The volt is derived from current and re- 

E 
sistance in accord with Ohm's law, C = — . The international 



THEORY OF THE HYDROGEN ELECTRODE 155 

volt is therefore denned as "the electrical pressure (electromotive 
force) which, when steadily applied to a conductor the resistance 
of which is one international ohm, will produce a current of one 
international ampere." 

F, the faraday, is derived for the international system as fol- 
lows. The international ampere deposits silver at the rate of 
0.00111800 of a gram per second. Since the atomic weight of 
silver is 107.88, a gram equivalent would be deposited in one sec- 
ond by 96494 amperes. The coulomb (international) is the quan- 
tity of electricity transferred by a current of one international 
ampere in one second. Hence 96494 coulombs are carried by a 
gram equivalent of silver and this is the value of the faraday in the 
international system. 1 

Returning now to equation (28) we know that R, the gas con- 
stant, is derived from the gas equation 

P V P V 

PV = -£ili T, where -±°12- is R. 

273.09 273.09 

V , the volume of 1 gram molecule of an ideal gas at one at- 
mosphere pressure and 0°C. is 22412 ± 2 cc. (Berthelot, 1904). 
P = one atmosphere or 76 cm. of mercury at 0°C. and 45° lati- 
tude. Since the acceleration of gravity at 45° latitude was taken 
to be 980.665 cm. per second when the "atmosphere" was defined, 
and, since 1 cc. mercury under the action of such a gravitational 
pull weighs 13.59545 grams, P = 980.665 X 76 X 13.59545 or 
1013276 dynes per square centimeter. 

„ „ . 1013276X22412 ooiCWifto 

Hence R is = 83157719.8 ergs. 

273.09 

10 7 ergs = one joule absolute. One joule, absolute = 0.99966 
international joule. Hence R = 8.3129446 international joules, 
or volt coulombs. 

From the derivations outlined above our equation reduces to 
the numerical form 

^ 8.3129446 T . C 
E = In — 

96494 n C 1 
1 The absolute value is approximately 96,500 (Vinal and Bates, 1914). 



156 THE DETERMINATION OF HYDROGEN IONS 

Transposing to Briggsian logarithms (to the base 10) by di- 
viding by 0.43429 we have 

E = 0.00019837 -log — (29) 

n C 1 

In the case of the hydrogen electrode, where the valence of the 
ionic hydrogen concerned is one, n is generally not written. 

A table of the values of 0.00019837 T for various tempera- 
tures is given in the Appendix. 

The significance of the equation for the concentration chain is 
that, if T is known, and if the concentration of the ions in the 
other solution is known, then the concentration of the ions in one 
solution can be determined from the E. M. F. of the chain. Fun- 
damentally there is no other way of applying electromotive force 
determinations to the estimation of ion concentrations, unless 
there can be brought to bear mass action relations. This makes 
it necessary to start somewhere in the system with a solution 
whose hydrogen ion concentration has been determined by an 
independent method. 

Let us assume for the moment that the conductivity method 
will give us correct information upon the hydrogen ion concen- 
tration of some simple solution such as that of HC1. 

It will be remembered that hydrogen ion concentrations are 
expressed in terms of normality, a solution normal with respect 
to hydrogen ions being one which contains in one liter of solu- 
tion 1 gram 2 of hydrogen ions. 

If, then, the normality of the hydrogen ion concentration in 
any unknown solution is to be determined it would seem that 
the most convenient solution with which to compare the unknown 
would be a solution of normal hydrogen ion concentration. Be- 
tween a hydrogen electrode in this standard and a hydrogen elec- 
trode in the unknown solution of hydrogen ion normality Cx 
there would be a difference of potential, E, given by the equation 

E = 0.000, 19837 T log -^ (30) 

Cx 

2 It makes little difference whether we regard the atomic weight of 
hydrogen as 1.0 or as 1.008 for the purpose at hand. 



THEORY OF THE HYDROGEN ELECTRODE 157 

A measurement of E and T would give Cx. Now E in the 
above equation is the difference between the potential difference 
at the one hydrogen electrode and the potential difference at 
the other hydrogen electrode. Nothing need be known about 
the value of either single potential difference and very little is 
known. If the electrode in the normal solution is made the 
standard it is obviously convenient for present purposes to call 
the potential difference between this electrode and the solution 
zero. Thus arises the definition: The 'potential difference between 
a hydrogen electrode under one atmosphere pressure of hydrogen and a 
hypothetical solution normal with respect to the hydrogen ion shall 
be considered to be zero at all temperatures} 

Having established by definition the value of the potential 
difference at the normal hydrogen electrode it becomes convenient 
to speak of the potential difference at any other hydrogen elec- 
trode as the hydrogen electrode potential, thus abbreviating the 
term "potential difference." It is, of course, implied that such 
a "potential" is referred to the potential difference at the normal 
hydrogen electrode. To indicate this the symbol Eh is used. 

Unfortunately it has* been necessary to introduce into the 
definition of the normal hydrogen electrode the phrase u hy- 
pothetical solution normal with respect to the hydrogen ion." 
This is because that very desirable standard solution would have 
to be prepared by means of "strong" acids and the estimation 
of the hydrogen ion concentration would fall under those uncer- 
tainties which have already been mentioned in a previous chapter. 
The difficulty is not entirely obviated by making the experimental 
standard a more dilute solution of a strong acid as has been done; 
but we shall leave to Chapter XIX further discussion of this 
Droblem, and, for the moment, we shall assume that there can be 
constructed from measurements such as those of the conductivity 
nethod a solution having a definite, known hydrogen ion con- 
centration. We could proceed with this, using it as one of two 
iolutions in a hydrogen gas cell, and applying to this cell the 

3 In various places, notably in the report of the Potential Commission 
>f the Bunsen-Gesellschaft (Abegg, Auerbach and Luther, 1910) it is not 
pecifically stated that this difference of potential shall be zero at all tem- 
peratures, but it seems to have been so understood and is specifically so 
; tated by Lewis (1913). 



158 THE DETERMINATION OF HYDROGEN IONS 

formula relating the E. M. F. to the ratio of the known to the 
unknown hydrogen ion concentration. But it is more convenient 
to use as a working-standard a calomel half cell (see Chapter 
XIII). When this is joined to a hydrogen electrode to form a 
calomel-hydrogen cell we need to know the difference of poten- 
tial between the calomel half cell and some known hydrogen elec- 
trode. Then we can correct the observed E. M. F. by this differ- 
ence and consider the corrected E. M. F. to be as if it were that 
between two hydrogen electrodes. 

Remembering that the mercury of the calomel half cell is posi- 
tive to the platinum of the normal hydrogen electrode and that 
the platinum of a hydrogen electrode becomes more negative 
the more dilute the hydrogen ion concentration, we have the scheme 
shown below 



8 a 

O O ml 

p, a ai Total 
3 * "' E.M.F. 

o JS 

J .2 

< * 



-Mercury of calomel electrode 

Eh of calomel electrode 
— Pt of normal hydrogen electrode 
Ehx of hydrogen electrode X 

-Pt of fractional normal hydrogen 
electrode X 



If E. M. F. is measured and E h is known, the value of E hx 
is at once obtained. This is the difference of potential between 
two hydrogen electrodes and equation (29) applied. In its work- 
ing form this equation is: 

E.M.F. (observed) - E h (of calomel half cell) _ . 1 = H ,^s 
0.000,198,37T ~ [H+] 

The above equation is still incomplete because we have not taken 
into consideration the liquid junction potential differences which 
exist wherever two unlike solutions are brought into contact. Nor 
have we yet considered the effect upon the potential difference at a 
hydrogen electrode of a change in the pressure of hydrogen from 
the one atmosphere partial pressure specified for the normal hy- 
drogen electrode. These two will be considered from the point 
of view of corrections to be made. Liquid junction potential 
differences, because of their distinct importance, will be treated 
in a separate chapter. 



THEORY OF THE HYDROGEN ELECTRODE 159 



BAROMETRIC CORRECTION 

The potential difference between a metal and solution will 
vary somewhat with the condition of the metal. A hammered, 
twisted or scratched electrode may show a different potential 
against a given concentration of its ions than will an electro- 
lytically deposited metal. In the case of the hydrogen electrode 
it seems to make little difference whether the hydrogen be held 
in platinum, palladium or iridium but it does make a consider- 
able difference if the surrounding pressure of hydrogen varies. If 
we have two hydrogen electrodes immersed in the same solution 
at the same temperature but under different pressures of gaseous 
hydrogen, we may assume that the concentration of the hydrogen 
in one electrode is different from that in the other electrode, and 
that the potential difference may be expressed as 

E = Ex-E 2 = — ln [ -5li (32) 

nF [H] 2 

in which equation R, T, n, and F have their customary signifi- 
cances and [H]i and [H] 2 are concentrations of atomic hydrogen in 
the electrodes (platinum black). Since n, the valence of hydro- 
gen, is 1, it may be omitted. 

We may now assume that there is an equilibrium between the 
molecular hydrogen about the electrode and the atomic or ionic 
hydrogen in, or issuing from, the electrode. This equilibrium 
may be expressed in accordance with the mass law as follows : 

rxr] y rTTl 

— = K t where [H] = concentration of atomic hydrogen 

[H 2 ] 

and [H 2 ] = concentration of molecular hydrogen 

Whence, 

[H] = VkS] (33) 

Substituting (33) in (32), we have 

E- RT ln VKOH^ _ RT^tH^ 
F VK t [H 2 ] 2 " 2F [H 2 ] 2 

It should be noted that the factor 2 in this equation does not 
:ome from giving hydrogen an effective valence of 2, as has often 
)een stated, but from the introduction of equation (33). We 



160 THE DETERMINATION OF HYDROGEN IONS 

might however derive the equation more directly by the energy 
relations and then the factor 2 would enter by reason of the vol- 
ume change involved. 

If the ratio of pressures is equal to the ratio of gas concentrations 

E = — ln^? 
2F P H2 

If P' H , be one atmosphere and P H2 be expressed in atmospheres 

tp RT, 1 

E = In — , OA , 

2F P H1 (34) 

This is the equation for the difference of potential between a 
hydrogen electrode under one atmosphere pressure of hydrogen 
(e.g., the normal hydrogen electrode) and a hydrogen electrode 
under pressure P H2 . 

Experimental justification of this equation is found in the 
experiments of Czepinski, Lewis and Rupert, Lewis and Randall, 
Lewis and Sargent, Ellis, Loomis and Acree and others. 

Hainsworth and Maclnnes have studied the effect of pressures 
up to 400 atmospheres and taking account of the volume changes 
of Hg, calomel, etc. which are negligible for smaller differences 
in pressure, they find a linear relation except for a slight deviation 
at the higher pressures. 

Several writers have felt constrained to emphasize the fact that 
in determining the hydrogen pressure from barometer readings 
they have subtracted the vapor pressure of the solution. The 
emphasis is still advisable, for a considerable number of precise 
hydrogen electrode data are published with corrections for baro- 
metric pressure on the basis that the normal hydrogen electrode 
pressure is one atmosphere including the vapor pressure of the 
solution. Corrections should be made to one atmosphere pres- 
sure of hydrogen, or else the standard used should be distinctly 
specified. 

Clark and Lubs (1916) have suggested that a more consistent 
standard than that now recognized for the normal hydrogen elec- 
trode would be obtained by defining a standard concentration of 
hydrogen father than a standard pressure. They used the com- 
monly accepted "standard condition" of a gas which is the con- 



THEORY OF THE HYDROGEN ELECTRODE 161 

centration at 0°C. and 760 mm. pressure. This would bring both 
the hydrogen and the hydrogen ions to a concentration basis, 
whereas now the one is expressed in terms of concentration and 
the other in terms of pressure. 
In applying the correction, 

T? RT, 1 

E b ar. m 



2F P H , 

it will be remembered that a decrease of the hydrogen pressure 
may be considered as a decrease of the electrolytic solution 
tension of the hydrogen. Hence under decreased hydrogen pres- 
sure the electrode is left more positive. 
In the cell 

Hg | Hg 2 Cl 2 KCl | H+ | Pt | H 2 

if the hydrogen is under diminished pressure the E. M. F. of the 
cell is too low. Hence the correction must be applied to make the 
E. M. F. larger than observed. Equation (31) becomes: 

E. M. F. + E (bar .) — E( ca i ome ]) __ jt (ok) 

.0.00019837 T 

To aid in the calculation of pressure corrections it is convenient 
to plot a curve giving the millivolts to be added to the observed 
E. M. F. for various corrected partial pressures. Tables of correc- 
tions from which a chart may be plotted are given in the Appen- 
dix. In these tables the barometer pressures given are the cor- 
'ected pressures. If hydrogen escapes from about the hydrogen 
ilectrode through a trap or other device which exerts back pres- 
sure, this pressure must be taken into consideration. Otherwise 
t is assumed that the pressure of the hydrogen is that of the 
urometer less the vapor pressure of the solution. To obtain the 
orrected barometer reading the instrumental calibration of the 
instrument is first applied, then the temperature correction (a 
■ able of which is given in the Appendix) necessary to bring the 
1 eight of the mercury column at temperature t to its height at 
1 amperature 0°C. Then there remains the correction for locality 
( see tables in Landolt-Bornstein) in order that the pressure may 
1 e reduced to the common basis of the "atmosphere," namely, the 
I ressure of 760 mm. mercury where the acceleration of gravity is 



162 THE DETERMINATION OF HYDROGEN IONS 

980.665 cm. per second. The last correction is of significance 
only for very accurate measurements and exceptional localities. 

For all ordinary cases it may be assumed that the vapor pres- 
sure is that of pure water at the temperature indicated. 

If the unit pressure is one atmosphere, the partial pressure 
must be reduced to atmospheres. 

As inspection of the table in the Appendix will indicate, the 
barometric correction may be neglected in rough measurements. 

REFERENCES 
General 

Abegg-Auerbach-Luther (1911), Bose (1900), Carhart (1911), Fresenius 
(1912), Foa (1906), Hardman-Lapworth (1911-12), Jahn (1901), 
Kistiakowsky (1908), Lewis, G. N. (1908, 1913), Lewis-Randall 
(1914), Lewis, W. K. (1908), Loven (1896), Michaelis (1910, 1911, 
1914), Myers-Acree (1913), Nernst (1889, 1916), Nernst-Wilsmore 
(1900), Noyes, Ostwald (1891), Rothmund (1894), Smale (1894), 
Stieglitz (1917), Wilsmore (1900). 

Gas Constant, R 
Berthelot (1904), Nernst (1904), Van Laar (1893, 1921). 

Value of the faraday 

Vinal-Bates (1914). 

Barometer correction 

Bose (1900), Czepinski (1902), Ellis (1916), Foa (1906), Hainsworth-Mac- 
Innes (1922), Lewis, W. C. (1920), Lewis-Randall (1914), Lewis- 
Rupert (1911), Lewis-Brighton-Sebastian (1917), Loomis (1915), 
Loomis-Acree (1916), Loomis-Myers-Acree (1917), Ostwald (1893), 
Smale (1894), Wilsmore (1901), Wulf (1904). 

Condition of hydrogen in electrodes and catalytic activation 

Berry (1911), Eggert (1915), Freeman (1913), Harding-Smith (1918), 
Hemptinne (1898), Hoitsema (1895-6), Holt (1914), Holt-Eggar-Firth 
(1913), LeBlanq (1893), Luther-Brislee (1903), Maxted (1919-1921), 
Mond-Ramsay-Shields (1898), Winkelmann (1901). 

Null point of potential 

Abegg-Auerbach-Luther (1909-1911), Brunner (1909), Freundlich-Makelt 
(1909), Goodwin-Sosman (1905), Lorenz (1909), Lorenz-Mohn (1907), 
Nernst (1897), Ostwald (1900), Palmaer (1898, 1907), Wilsmore- 
Ostwald (1901). 



CHAPTER XI 
Potential Differences at Liquid Junctions 

When two unlike solutions of electrolytes are brought into con- 
tact there develops at the junction a potential difference. Since 
no important chain can be constructed without involving such a 
liquid junction potential, it is of great importance to know the 
cause so that the magnitude of the potential may be calculated 
or ways devised for its reduction. 

The principal cause of the potential difference was attributed 
by Nernst to unequal rates of diffusion of ions across the plane 
of junction. 

It has been found in the study of electrolytic conduction that 
under uniform potential gradient different ions move through a 
solution with different velocities. The following table taken from 
Lewis' A System of Physical Chemistry shows the velocities of a 
number of ions in aqueous solution under a potential gradient 
of one volt per centimeter. Since in each case the potential gra- 
dient is the same and the ionic charge the same it is evident that 
the order in which the velocities stand in the table is the order 
in which the velocities of free movement will stand. 



ION 


ABSOLUTE VELOCITY 

IN CENTIMETERS PER 

SECOND. 18°C. 


ION 


ABSOLUTE VELOCITY 

IN CENTIMETERS PER 

SECOND. 18°C. 


H 


32.50 10"* 
6.70 10"* 
4.51 10-* 
3.47 10"* 
5.70 10"* 


OH 


17.80 10~* 


K 


CI 


6.78 10"* 


Na 


N0 3 


6.40 10-* 


Li 


CH s COO 


3.20 lO -4 


Ag 











Let it now be assumed that a solution of hydrochloric acid is 
placed in contact with pure water of negligible ion content at an 
imaginary plane surface. Independently of one another the 
ihlorine and the hydrogen ions will tend to migrate across the inter- 
'ace and into the water. As shown in the above table the velocity 
)f the hydrogen # ion under the influence of a potential gradient 

163 



164 THE DETERMINATION OF HYDROGEN IONS 

is much greater than the velocity of the chlorine ion under the 
same gradient, and the relative velocities of free movement must 
therefore be in the same proportion. Consequently there will 
be established on the water side of the plane an excess positive 
charge. This charge will increase until the electrostatic attrac- 
tion dragging the slower moving chlorine ions brings them to the 
velocity of the hydrogen ions. When this state is reached, as it 
is almost instantaneously, there is established a steady potential 
difference at the liquid junction. If the water is replaced by a 
solution of an electrolyte, we have not only the chlorine and the 
hydrogen ions migrating across the boundary into this new solu- 
tion, but the ions of this solution migrating into the hydrochloric 
acid solution. 

In the comparatively simple case where two solutions of differ- 
ent concentration of the same binary electrolyte are placed in 
contact the following elementary treatment may be used. Let 
the concentration of the ions on one side of the interface be C 
and on the other side be a lesser concentration C 

When migration has established the steady potential E let it 

be over an interface of such extent that E is due to the separation 

of one faraday. If that fraction of the separated charge which 

is carried by the anion is n a the work involved in the transport of n a 

C . 

equivalents from C to C is n a RT In ^>. Likewise if that fraction of 

the charge carried by the cations is n c the work involved in the 

C 

transport of n c equivalents from C to C is n c RT In p7,. The 

work involved in the separation of the ions as they migrate from 
the high to the low concentration is 



n a RTln— - n c RTln— = EF 

c c 



Whence 



E = (n. - n c ) — In — or (n - n a ) —-In — (36) 

F C r C 

according to which ion moves the faster. 

Now the ions being univalent, n a , the fraction of the charge car- 
ried by the anion, is equal to the fraction N of one equivalent of 
anions transported from the cathode to the anode section. Like- 



POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS 



165 



wise n is 1-N. The ratio of N to 1-N is equal to the ratio of 
the absolute velocities of the ions. 

N velocity of anion (V a ) 



1 — N velocity of cation (V c ) 



Whence 



and 



N = 



V a + V, 



1-N = 



V a + V, 
Substituting N for n a and 1 



, transport number of anion, 



, transport number of cation. 
N for n c in equation (36) 



E= (V a _- L Ve) RT ln C 
(V a + V ) F C 



(37) 



Lewis and Sargent (1909) have treated the special case of two 
equally concentrated solutions of two binary salts having one ion 
in common. Substituting equivalent conductivities as propor- 
tional to mobilities they obtain 



E^ln^i 
F X 2 



(38) 



where Xi and X 2 are the equivalent conductivities of two solu- 
tions. Applying this equation they obtain the following corre- 
spondence between calculated and observed values of E, the 
liquid junction potential. 



SOLUTIONS IN CONTACT 


E (observed) 


E (calcu- 
lated) 


E (OBS.)- 
E (CALC.) 


).2nKC1-0 2nKC 2 H 3 0, 

).1nKC1-0.1n KC 2 H 3 2 

).2nKC1-0.2n KOH 


-0.0080 
-0.0074 
+0.0170 
+0.0165 
+0.0004 
+0.0192 ±0.0003 
-0.0286 


-0.0082 
-0.0077 
+0.016S 
+0.0165 
+0.0004 
+0.0187 
-0 0286 


0.0002 
0.0003 
0.0002 


).1nKC1-0.1nKOH 


0.0000 


).2n KC1-0.2n KBr 


0.0000 


).2n NuC1-0.2n NaOH 

I. In KCI-O.In HC1 


0.0000 







In the more general case limited chiefly by the condition that 



166 THE DETERMINATION OF HYDROGEN IONS 

all the ions shall have the same valency Planck (1890) deduced 
the equation: 

E - 5^ ln ^ (39 ) 

wF 

where E is the contact difference of potential in volts and £ is 
defined by the equation: 

ln?- 2 -ln£ 
SU 2 - Ui m C! i gc 2 - ci 

V *-^ In^ + ln/ 02 "^ 1 

Ci 

Ci is the sum of the concentrations of cations and anions in the 
more dilute solution and c 2 the sum in the more concentrated solu- 
tion, w is the valency, R the gas constant, F the faraday, and 

Ui = uV + u"c" + . . . . 
V, = vV + v"c" + . . . . 

and U2 and V 2 are similar sums for the second solution. The u' 
and v' symbols represent the ion mobilities and the c' symbols 
the corresponding ion concentrations. 

Besides the limitation noted above this equation is strictly ap- 
plicable only to very dilute solutions where dissociation is complete 
and it was deduced for the condition of a sharp boundary such 
as is not realized in experimental work. 

P. Henderson (1907, 1908) therefore considered the connecting 
boundary as a series of mixtures of the two solutions in all propor- 
tions and deduced a somewhat simpler equation which Cumming 
(1912) has modified by introducing the mobilities at the different 
concentrations used. 

It is of course obvious that the equations given above and many 
others of like nature are inapplicable when the solutions placed 
in contact are of unknown composition or are very complex. 
Br0nsted (1922) has proposed a novel method of approach which 
may prove to have some value, but as yet it is untried, and we 
are forced to get such comfort as we can find in a deduction from 
the above treatment which will be considered presently. But 
even in the simple cases where one or another of the equations 



POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS 167 

apply the experimenter must face the difficulty of maintain- 
ing experimentally the conditions for which they were set up. 
For instance Chanoz (1906) constructed the symmetrical 
arrangement : 

Electrode II MR I M'R' I MR II Electrode, 
A B 

and then, by maintaining a more or less sharp boundary at A by 
renewal of the contact, and allowing diffusion to occur at B, he 
obtained very definite E. M. F.'s instead of the zero E. M. F. 
which the symmetrical arrangement demanded. This time effect 
has been noted by Weyl (1905) and has since been frequently 
reported, for instance, by Bjerruni (1911), Lewis and Rupert 
(1911), Cumming and Gilchrist (1913), Walpole (1914) andFales 
and Vosburgh (1918). 

Since the change of potential has been ascribed to the diffusion 
and mixing which alter the distribution of the contending, mi- 
grating ions, it has seemed to many that the effect could be made 
more uniform and conditions more reproducible if the solutions 
were brought into contact at a membrane. This would tend to 
prevent mixing. Sand or other material would also delay the 
mixing and the diffusion. Cumming and Gilchrist (1913) used 
a symmetrical chain such as that of Chanoz (see above) , and found 
that when a membrane was introduced at A while ordinary con- 
tact was allowed at B the symmetry of the chain was destroyed. 
Prideaux (1914) also found a difference when the contact was 
made in the one case with, and in the other case without, a parch- 
ment membrane. On considering this case and others in which 
the constituents of the membrane may take part in the establish- 
ment of the potential, he came to the conclusion that there were 
phenomena concerned which made the application of the ordinary 
squations of dubious value. See also Beutner (1913). 

Lewis, Brighton and Sebastian (1917) using Bjerrum's (1911) 
suggestion of a layer of sand in which to establish the liquid con- 
act found that "at no time were reproducible results obtained 
lor results which remained constant to 0.0001 volt for more than 
i minute or two. The potential of the liquid junction first es- 
ablished was surprisingly high (0.030 volt) and fell rapidly with- 



168 THE DETERMINATION OF HYDROGEN IONS 

out reaching any definite limiting value. " The liquids placed in 
contact in this experiment were 0.1m HC1 and 0.1m KC1. These 
authors abandpned the sand method. 

On the other hand Myers and Acree (1913) report satisfaction 
with Bjerrum's " Sandfiillung. " 

Other devices such as the use of a wick have been resorted to, 
but on the whole direct liquid contact is considered the best. 

Recently Lamb and Larson (1920) have described the "flowing 
junction" which they find to be much more reproducible than 
the junctions usually made. They conclude "that a 'flowing' 
junction, obtained simply by having an upward current of the 
heavier electrolyte meet a downward current of the lighter elec- 
trolyte 1 in a vertical tube at its point of union with a horizontal 
outflow tube, or by allowing the lighter electrolyte to flow con- 
stantly into a large volume of the heavier electrolyte, even with 
N solutions, gives potentials constant and reproducible to 0.01 of 
a millivolt. " The device used by Lamb and Larson is illustrated 
in figure 15. 

Maclnnes and Yeh (1921) have improved the system of Lamb 
and Larson and have confirmed the principle that reproducible 
liquid junction potentials may be thus obtained, but they find 
most interesting effects with different rates of flow. Of particular 
importance is the observation that the reproducible potentials 
are not the highest that can be obtained. 

It is encouraging to see experimental work of this type being 
done for those who are interested in the general applications of 
electrode measurements cannot escape the feeling that the ex- 
perimental side of the problem has been too much neglected. 

A most important contribution to experimental methods of 
handling liquid junction potential differences arose from the the- 
ory of Nernst that the potential is due to the unequal migration 
of ions. The table of velocities given on page 163 will show that 
if KC1 is concerned no large potential can arise from the partici- 
pation of its ions, because they move with about the same velocity. 
If such a salt be present in high concentration upon both or even 
one side of the interface, the electrostatic fields of its ions will 
dominate the situation, and, migrating at equal velocities, will tend 
to maintain zero junction potential difference. Bjerrum (1911) 
studied the potential differences developed when concentrated so- 



POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS 



169 



lutions were thus employed and estimated the theoretical values 
with the aid of Planck's formula and with that of Henderson, 
which purports to take into account the effect of the destruction 
of a sharp boundary. He came to the conclusion that the use 
of a 3.5m KC1 solution would not completely eliminate the po- 
tential against hydrochloric acid solutions but he suggested a 
more or less empirical extrapolation which would, he thought, 




Fig. 15. Lamb and Larson's Device for the Flowing Junction 

j ive the proper correction. The correction is the difference in the 
] 1. M. F/s of a chain found when first 3.5m KC1 is used and then 
> men 1.75m KC1 is used to connect two electrodes. 

More recently Fales and Vosburgh (1918) have made an ex- 
t msive comparison of various chains, and with the aid of Planck's 
f )rmula to give the order of magnitude of various contact poten- 
t als, thay have attempted to assign values which will lead to a 
g 3neral consistency. They concur with others in finding Planck's 
f irmula invalid in the assignment of accurate values to liquid 
j motions, such as: 



170 THE DETERMINATION OF HYDROGEN IONS 

"xm KC1 - 1.0m HC1 and xu KC1 - 0.1m HC1 where x ranges 
from 0.1 to 4.1 and the temperature is 25°C." 

They conclude that "there is no contact potential difference at 
25° between a saturated solution of potassium chloride (4.1m) and 
hydrochloric acid solutions ranging in concentrations from 0.1 
molar to 1.0 molar," confirming the suggestion of Loomis and 
Acree (1911). 

Because of the great detail concerned in the reasoning of Fales 
and Vosburgh it is impossible to briefly summarize their work, but 
before their conclusion can be considered valid it must be noted 
that they themselves point out that "in an electromotive force 
combination having a contact potential difference as one of its 
component electromotive forces, the diffusion across the liquid 
junction of the one liquid into the other brings about a decrease in 
the magnitude of the contact potential difference, and this de- 
crease may amount to as much as one-tenth of the initial magni- 
tude of the contact potential difference. " This experimental un- 
certainty undoubtedly renders questionable the comparability, 
if not the precision of measurements by different experimenters. 
If so there may lurk in the data used by Fales and Vosburgh in 
their argument of adjustment to consistency an indefinite degree 
of incomparability. 

Indeed the whole subject of contact potential is still in an un- 
satisfactory state. The experimental uncertainties which have 
been revealed have sometimes been overlooked in the calculation 
of important electrode values. Some of these values will be dis- 
cussed in Chapter XIX. 

In writing the components of a chain it is customary to desig- 
nate the situation of a potential difference by a single line and 
the position of a potential difference which is to be left out of 
consideration by a double line. Thus 

Pt H 2 1 N/10 HC1 1 N/10 KC1 Hg 2 Cl 2 1 Hg 

indicates that there are potential differences at the positions 
shown by the lines; while if the above chain is written as 

Pt H 2 1 N/10 HC1 1| N/10 KC1 Hg 2 Cl 2 |Hg 

the double line indicates that the liquid junction potential differ- 
ence is to be left out of consideration in formulating the E.M.F. 



POTENTIAL DIFFERENCES AT LIQUID JUNCTIONS 171 

It now remains to determine if possible the order of magnitude 
of the contact differences of potential entering into chains used 
in the study of physiological solutions and the buffer solutions of 
the colorimetric method. 

Since the concentrations of the hydrogen and the hydroxyl ions, 
which are the most mobile of all ions, are very low in most of these 
solutions, the contact potential difference may be expected to be 
much less than that found in hydrochloric acid solutions and sim- 
ilar solutions of high hydrogen or hydroxyl ion concentrations. 
It is the customary practice to employ saturated KC1 in making 
the junction or to make the junction first with 3.5m, then with 
1.75m KC1 and extrapolate according to Bjerrum. The extra- 
polation so indicated generally amounts to only a few tenths of a 
millivolt, and in certain cases such as "standard acetate" to only 
0.1 millivolt. Although such an extrapolation may be too low or 
too high its magnitude indicates that the error is not large. 
Furthermore there is found experimentally a drift in contact 
potential difference with time which is very much less than that 
found, for instance, at the junction sat. KC1— 0.1m HC1. There can 
be no doubt that this is indicative of a low potential difference. 

As pointed out by Clark and Lubs (1916), it is the difficulty in 
dealing with the contact potential of hydrochloric acid solutions 
that renders them unsuitable for routine standardization of 
hydrogen electrodes. 

Practical conclusions reached by experimentation are: 

1. For precise E. M. F. measurements combinations having 
small liquid junction differences of potential should be used as 
far as is practicable. 

2. It should be recognized that the E. M. F. of a cell which 
derives part of its E. M. F. from a liquid junction potential dif- 
ference varies with the time elapsing after the formation of the 
liquid junction. Consequently this time should become a part 
of the data to be recorded. 

3. It is preferable that measurements of E. M. F. be made 
directly after the formation of or the renewal of the liquid junction. 

4. Since the liquid junction potential difference may vary with 
the manner of its formation the effort should be made to effect this 
junction in a reproducible way. 

5. Reproducible potential differences are given by the flowing 
junction in the cases so far tried. 



172 THE DETERMINATION OF HYDROGEN IONS 

6. Narrow or capillary tubes at the point of liquid junction 
should be avoided. 

7. An apparatus which permits the renewal of a junction and 
its complete removal when cells are left set up together for some 
time is preferable to any device such as membranes to protect the 
diffusion of solutions into electrode spaces. 

8. Membranes at the liquid junction are to be avoided. 

9. Wherever permissible saturated KC1 solution should form 
one side of a liquid junction. 

10. When a concentrated KC1 solution is used to make liquid 
junction it should be stated whether the Bjerrum extrapolation 
with the use of 3.5m and 1.75m KC1 has been employed or whether 
saturated KC1 was used without the Bjerrum extrapolation. 

REFERENCES 

Abegg-Bose (1899), Beutner (1912), Bjerrum (1905, 1911), Chanoz (1906), 
Clarke, W. F.-Myers-Acree (1916), Cremer (1906), Cumming (1912), 
Cumming-Abegg (1907), Cumming-Gilchrist (1913), Donnan (1911), 
Fales-Vosburgh (1918), Gouy (1916), Ferguson (1916), Henderson, P. 
(1907-1908), Lamb-Larson (1920), Lewis-Sargent (1909), Lewis- 
Rupert (1911), Loomis-Acree (1911), Loven (1896), Maclnnes (1915), 
Maclnnes-Yeh (1921), Melander (1915), Myers-Acree (1913), Neg- 
baur (1891), Nernst (1888), Planck (1890), Pleijl (1916), Prideaux 
(1914), Reisenfeld (1901), Sackur (1901), Schwyzer (1914), Tower 
(1896), Weyl (1905). 



CHAPTER XII 

Hydrogen Electrodes and Electrode Vessels 

For the most part the base of a hydrogen electrode is simply a 
piece of platinum foil or wire. If wire is used an end is fused 
into a glass tube carrying mercury to form a convenient means 
of making contact with the lead of the potentiometer circuit. 
The wire may then be wound upon a machine screw to give it a 
neat form. If foil is used a piece about 1 sq. cm. is first welded 
to a short piece of No. 30 B. S. gauge platinum wire by tapping 
the two smartly with the flat end of a punch while they are laid 
upon a flat hard surface in the white heat of a blast lamp. Next 
draw off a glass tube to a thin, blunt point and break away the 
capillary until the wire will enter. Slip the wire in until the foil 
touches the glass. Then, holding the wire with foil uppermost, 
rotate the tube with the junction in the tip of a fine flame. Let 
the glass fuse until a perfect seal is made and a little of the glass 
fuses to the edge of the foil. The steps are illustrated in figure 
16. It is important to avoid a seal with too thin a glass junc- 
tion, for such a seal will easily crack. It is likewise important 




Fig. 16. Construction of Simple Electrode 

to avoid too heavy a junction for proper annealing then becomes 
difficult. To anneal hold the electrode directly after its construc- 
tion in a smoky flame and gradually remove to cooler and cooler 
parts of the flame. If a light but substantial junction is made 
with the edge of the foil the electrode will be rugged. 

In place of the platinum foil gauze is sometimes successfully 
used. The advantage is a larger surface; but gauze will make a 
careful technician nervous over the problem of thoroughly clean- 
ing the crevices. 

173 



174 THE DETERMINATION OF HYDROGEN IONS 

It is sometimes assumed that complete equilibrium can be at- 
tained only when the hydrogen in the interior of the metal sup- 
porting the platinum black is in equilibrium with that on the, 
surface. To reduce the time factor of this soaking-in process it 
is considered advantageous to use as the supporting metal a very 
thin film of platinum or iridium deposited upon glass. Doubt- 
less the finest of such films could be deposited by holding the glass 
tangent to the Crookes' dark space of a vacuum discharge and 
spattering the metal on from electrodes under 5000 volts difference 
of potential. The method practiced is to burn the metal on from a 
volatile solvent. The recipe given by Westhaver(1905) is as fol- 
lows: 0.3 gram iridium chloride moistened with concentrated HC1 
is dissolved in 1 cc. absolute alcohol saturated with boric acid. 
To this is added a mixture of 1 cc. Venetian turpentine and 2 cc. 
lavender oil. The glass after being dipped in this solution is 
rotated while drying to give an even deposit. It should then be 
very carefully dried to prevent blistering during the ignition. 
On gradually heating over an alcohol flame there is at last produced 
a very thin film of iridium. The process should be repeated 
until a good conducting film is obtained. 

Gooch and Burdick (1912) have better success with a viscous 
mixture of pure chloroplatinic acid and glycerine. This is ap- 
plied with an asbestos swab to the glass which has previously 
been heated to a temperature which will instantly volatilize the 
glycerine. The resulting film is heated until it adheres well 
to the glass. 

Meillere (1920) gives the following recipe. 0.5 gram dry 
platinum chloride is triturated with 10 or 15 grams of essence of 
camomile. The mixture is thinned with about an equal volume 
of methyl alcohol. 

If after some practice it is found that even deposits can be 
formed by one or another of the methods, the next difficulty met 
is in obtaining good adherence of the film to the glass. This 
must be done by heating sufficiently but at the same time there 
must be avoided a fusion of such extent that the continuity of 
the metallic film will be destroyed. Such a fusion will be more 
easily avoided and at the same time volatilization of impurities 
in the film will be made easier because of the higher temperature 



HYDROGEN ELECTRODES 175 

permitted, if the glass support is made of a "hard" glass. How- 
ever, in the selection of such a glass one with a temperature 
coefficient of expansion approximately equal to the platinum 
should be selected, — chiefly as a provision for the next step which 
will now be described. 

The chief technical difficulty in the preparation of electrodes 
with the films described is in establishing the necessary electrical 
connection. An exposed platinum wire contact destroys the 
object in using the film. Ordinarily the electrode is made by first 
coating a bar of glass in the end of which there is sealed a plati- 
num wire and then fusing this bar into the end of a glass tube so 
that the platinum contact is exposed within the tube where 
mercury contact may be made. Connection with the film is made 
by the film of metal that runs through the glass seal. It is less 
clumsy to seal the wire into the end of a glass tube, break off 
the wire flush with the glass, coat the tube with the film and 
then close over the exposed wire with a drop of molten glass. 

A scheme which is said to partially accomplish the purpose 
of a thin film of supporting metal is to cover a platinum support 
with a gold-plate, gold being relatively impervious to hydrogen. 
It is doubtful whether this reason has much practical weight. 
However a gold-plate is of great advantage. If offers a surface 
upon which deposits of "black" adhere well. It forms a support 
easily dissolved by electrolysis in hydrochloric acid, thus provid- 
ing an easy means of removing old deposits. And the character 
of the gold deposit gives an additional means of testing the clean- 
liness of the electrode prior to blackening. 

For the gold plating of electrodes the following recipe may be 
used. Dissolve 0.7 gram gold chloride in 50 cc. water and pre- 
cipitate the gold with ammonia water, taking care to avoid an 
excess. Filter, wash and dissolve immediately in a KCN solution 
consisting of 1.25 grams KCN in 100 cc. water. Boil till the solu- 
tion is free from the odor of ammonia. 

DEPOSITION OF "BLACK" 

According to the work of earlier investigators and the con- 
sensus of opinion among more recent investigators there seems to 
be no difference under equilibrium conditions between coatings of 
platinum-, iridium- or palladium-black. No recent detailed data 



176 THE DETERMINATION OF HYDROGEN IONS 

are available however. Of the three, iridium is recommended by 
Lewis, Brighton and Sebastian because of its higher catalytic ac- 
tivity, and palladium by Clark and Lubs (1916) for use in the 
study of physiological solutions because of the relative ease with 
which one deposit may be removed before the deposition of the 
next in the frequent renewals which are often necessary. Pal- 
ladium black is easily removed by electrolysis in HC1. Deposits 
of platinum or iridium may be removed by electrolysis in HC1 
solution, if they are deposited upon a gold plate. 

One of the essentials for making good deposits is a very high 
degree of cleanliness of the electrode. • A good test is the evenness 
with which bubbles of hydrogen escape from the surface during 
electrolysis. Another essential in the preparation of a good elec- 
trode is that the deposit of black metal be not only even but of 
proper thickness. The inclination is to make the deposit too 
thick, with the production of a sluggish electrode. To obtain 
evenness of deposit it is necessary to hold down the dimensions 
of the electrode, provide more than one lead, or modify the rate 
of deposit. With this much said there remains very little system- 
atized information upon the composition of solutions and the 
current densities which are best for the deposition of the finely 
divided metal required. 

For the deposition of platinum black Ellis (1916) uses a solution 
of pure chloroplatinic acid containing 1 per cent Pt. He cau- 
tions against the use of the lead acetate which has come down to 
us in recipes for the deposition of platinum black upon electrodes 
for conductivity measurements. For the deposition Ellis uses a 
small auxiliary electrode and a current large enough to liberate 
gas freely at both electrodes. He continues the deposition with 
five-minute reversals of current for two hours and obtains a very 
thick coating. The author prefers an adherent, even, thin de- 
posit sufficient to just cover the glint of metal beneath. In com- 
parison of one against another in the same solution such thin de- 
posits are found to agree within 0.02 millivolt. They may be 
deposited within a minute from the solutions used by the author. 

For the deposition of iridium Lewis, Brighton and Sebastian 
(1917) make the gold or gold-plated electrode the cathode in a 
5 per cent solution of iridium chloride. "The best results were 
obtained with a very small current running for from twelve to 



HYDROGEN ELECTRODES 177 

twenty-four hours. Too large a current gives a deposit which 
appears more like platinum black and which is easily rubbed off. " 

The author has used deposits of platinum, iridium and palla- 
dium upon platinum, upon gold-plated platinum and upon "rho- 
tanium" alloy. Acidified (HC1) 3 per cent solutions of the chlorides 
of each metal are used without much attention to the exact 
strength. The current from a four- volt storage battery is allowed 
to produce a vigorous evolution of gas. The. electrode is plunged, 
immediately after the deposition, into a dilute sulfuric acid solu- 
tion and electrolyzed. It is required that the bubbles of hydro- 
gen then escaping come off evenly, that the electrode be evenly 
covered with the deposit in thickness sufficient to cover the glint 
of polished metal, and that the deposit shall adhere under a vigor- 
ous stream of water. No electrode is ever subjected to blast 
lamp treatment as is sometimes recommended. Instead, renewals 
are made by removing the old deposit by electrolysis in HO 
solution, and, if any defect whatsoever develops to prevent a 
good redeposition after such electrolysis, the electrode is retired 
from duty. 

It must be admitted that the above description is loose. 
This is because the rush of experimental application has prevented 
a detailed examination of conditions, and experience has taught 
details difficult to formulate in exact language. No detailed 
descriptions have been found in the literature and those that are 
found are quite inadequate to account for the varied deposits some- 
times formed. One item which it would be interesting to investi- 
gate is the influence of the hydrogen ion concentration of the 
solution upon the character of the deposit. Since there is a 
simultaneous deposit of metal and hydrogen and, since the char- 
acter of the platinum, palladium or iridium black is undoubtedly 
due to the vigor of the hydrogen evolution, it is evident that the 
pH of the solution constitutes a -part of the conditions. 

It may be said however, that ordinarily there is little difficulty 
in obtaining an active deposit if the metal concentration is main- 
tained as the solution is used, if electrodes are kept thoroughly 
clean and if the solutions are kept free from even those impurities 
which collect as a film upon exposed solutions. To remove these 
films suck them off with a clean tube attached to a filter pump. 

The system used by the author for deposition of "black" is 



178 THE DETERMINATION OF HYDROGEN IONS 

as follows. A row of small vessels, such as weighing bottles 
about 2 cm. diameter and 5 cm. deep are fitted with electrodes. 
These electrodes are all attached through binding posts mounted 
on a wooden rail. These in turn are connected to one pole of 
a double-pole, double-throw switch. The opposite pole is con- 
nected with a flexible lead tipped with platinum. This lead is 
used to connect with the electrodes to be treated. Tl>e middle 
connections of the double-throw switch are connected with a 
4-volt storage battery. The other connections are cross-wired. 
One of the vessels is filled with hydrochloric acid made by a 
one-to-one dilution of ordinary 37 per cent acid. This is used 
to dissolve previous deposits with the aid of electrolysis (switch 
reversed, treated electrode +)• Another vessel is filled with 10 
per cent sulfuric acid for preliminary direct and counter-electrol- 
ysis in testing the cleanliness of the electrode. Another vessel 
is filled with the platinum, palladium or iridium chloride solution. 
When using palladium so-called reagent palladium is used as + 
electrode and this is removed from the solution when not in use. 
After deposition of the black the electrode under treatment is 
quickly placed under a vigorous stream of water and then elec- 
trolyzed in a another vessel of freshly prepared ten per cent sul- 
furic acid until thoroughly charged with hydrogen. 

When used with inorganic solutions which undergo no decom- 
position electrodes may often be used repeatedly, provided they 
are kept clean and not allowed to dry. When there is any sign 
or suspicion of an electrode becoming clogged, poisoned, worn, 
dry or in any way injured, there should be not the slightest hesi- 
tation in reblackening or even rejecting it. It is therefore not 
good practice to so tie up a particular electrode with an expensive 
stopper or vessel that there will be hesitation in rejecting it. 

HYDROGEN ELECTRODE VESSELS 

So many types of vessel have been published that it is diffi- 
cult to do justice to the advantages of each. The selection must 
depend in some instances upon the material to be handled, but in 
any case there are a few principles which it is hoped will be made 
clear by a discussion of a few of the more widely used vessels. 

The general method of operation is to partially or wholly im- 



HYDROGEN ELECTRODES 



179 



merse the electrode in the solution to be measured and then to 
bubble hydrogen through the vessel till constant potential is 
attained. The vessel described by Lewis, Brighton and Sebastian 
(1917) and illustrated in figure 17 is representative of the general 
type of vessel used for what may be called the classic mode of 
operation. The following is the quoted description of this vessel : 




Fig. 17. Hydrogen Electrode Vessel of Lewis, Brighton and 

Sebastian 

Hydrogen from the generator enters at A, and is washed in the bubbler 
B with the same solution that is contained in the electrode vessel. This 
efficient bubbling apparatus saturates the gas with water vapor, so that 
the current of hydrogen may run for a long period of time without changing 
the composition of the solution in the main vessel. The gas rises from the 
tip C, saturating and stirring the whole liquid from G to F, and leaves the 
apparatus through the small trap E, which also contains a small amount 
of the same solution. The platinum wire attached to the electrode D is 
sealed by lead glass into the ground glass stopper M. L is a joint made by 
fusing together the end of the platinum wire and the connecting wire of 
copper. The surface of the solution stands at the height F so that the 
iridium electrode is about one-half immersed. The apparatus from F 
through G, H, I to J is filled with the solution. With the form of construc- 
tion shown it is an easy matter to fill the tube without leaving any bubble? 



180 THE DETERMINATION OF HYDROGEN IONS 

of air. The reservoir K filled with the same solution serves to rinse out 
the tube I, J from time to time. The whole apparatus may be mounted 
upon a transite board, or for the sake of greater mobility, may be held in a 
clamp, the several parts being rigidly attached to one another to avoid 
accidental breakage. The whole is immersed in the thermostat about to 
the point L. 

The tube J dips into an open tube through which communication is made 
to other electrode vessels. This connecting tube may be filled with the 
same solution as is contained in the hydrogen electrode vessel or with any 
other solution which is desired. All measurements with acids are made 
with one of the stopcocks H, I, closed. These stopcocks are not greased 
and there is a film of acid in the closed stopcock which suffices to carry the 
current during measurement. In Order to make sure that no liquid poten- 
tial is accidentally established, the second stopcock may be closed up and 
the first opened. No difference of potential in acid solution has ever been 
observed during this procedure (but this is not true for solutions of salt 
and alkalies). If it is desired that both stopcocks be open, the same 
liquid that is in the electrode vessel is placed in the connecting tube at J 
and the stopcocks H and I are opened after the current of hydrogen has been 
cut off by the stopcock A, and the opening of the trap E has been closed. 

If hydrogen enters the cell at the rate of one or two bubbles per minute 
several hours are required for the saturation of the solution and for the 
removal of air. After this time the potential is absolutely independent of 
the rate of flow of hydrogen and the generator may be entirely cut off for 
many hours without any change. 

For some biochemical studies such a vessel is unsuitable. It 
is sometimes absolutely essential that equilibrium potentials be 
established rapidly. The necessity is perfectly apparent when one 
is dealing with an actively fermenting culture. It is not always 
so apparent when dealing with other solutions, but it is suspected 
that absolutely complete equilibrium is never attained in some 
complex biochemical solutions and that we have to depend upon 
speeding up the reaction between hydrogen and hydrogen ions till 
a virtual equilibrium point is attained (see Chapter XVII) . 

It was shown by Michaelis and Rona (1909) that a fairly con- 
stant E. M. F. is quickly attained, even in blood, if the platinized 
electrode, previously saturated with hydrogen, is allowed to merely 
touch the surface of the solution. This is probably due, as sug- 
gested by Hasselbalch (1913) and again by Konikoff (1913), to a 
rather sharply localized equilibrium at the point of contact. Re- 
ductions and gas interchanges having taken place within the small 
volume at the point of contact, diffusion from the remaining body 
of the solution is hindered by the density of the surface layer 
with which alone the electrode comes in contact. 



HYDROGEN ELECTRODES 181 

In exploring new fluids it appeared hazardous to the writer to 
rely upon such a device, which appears to take advantage of only 
a localized and hence a pseudo-equilibrium, and which makes no 
allowance for a possible difference between the solution and sur- 
face film in the activity of the hydrogen ions. Hasselbalch's 
(1911) principle seemed therefore to be more suitable. 

Hasselbalch found that a very rapid attainment of a constant 
potential can be obtained by shaking the electrode vessel. Un- 
der these conditions there should be not only a more rapid inter- 
change of gas between the solution, the gaseous hydrogen, and 
the electrode, an interchange whose rapidity Dolezalek (1899) 
and Bose (1900) consider necessary, but the combined or molec- 
ular oxygen, or its equivalent, in the whole solution should 
be more rapidly brought into contact with the electrode and there 
reduced. Furthermore, by periodically exposing the electrode the 
hydrogen is required to penetrate only a thin film of liquid before 
it is absorbed by the platinum black. The electrode should there- 
fore act more rapidly as a hydrogen carrier. For these reasons a 
true equilibrium embracing the whole solution should be rapidly 
obtained with the shaking electrode; and indeed a constant 
potential is soon reached. 

Eggert (1914-1915) in Nernst's laboratory made a study of the 
rapidity of reduction by hydrogen electrodes in which he com- 
pared the effect of alternate immersion and exposure to the hydro- 
gen atmosphere with the effect of continued immersion. In the 
reduction of metal salt solutions such as ferric salts he obtained 
a much greater velocity of reduction when the electrode was 
periodically removed from the liquid carrying a thin film of solu- 
tion to be exposed to the hydrogen. The maximum velocity 
was proportional to the platinum surface and the time of contact 
with the gas. It was independent of the number of times per 
ninute the electrode was raised and lowered. As the reaction 
leared completion the decrease in velocity of reaction became 
exponential. 

Making use of the principles brought out in the preceding dis- 
cission and also certain suggestions noted in the chapter on liquid 
unction potentials Clark (1915) designed a vessel which appears 
o have found favor for general use. A working drawing of this 
r essel is shown in figure 18. If solutions more viscous than fresh 



182 



THE DETERMINATION OF HYDROGEN IONS 



milk are to be used, the bores of the inlet and outlet tubes 
should be made larger. If only very small quantities of the solu- 
tions to be tested are available, the dimensions of the vessel 
may be reduced. In figure 19 is a diagrammatic sketch of the 
complete system now in use by the author for ordinary work. 



(ron no. o stopper) 




/eo° 



Fig. 18. A Hydrogen Electrode Vessel (Clark, 1915) 

Notes. In submitting this working drawing to a glass blower it shall be 
specified that: (1) Cocks shall be joined to chamber with a neat and wide 
flare that shall not trap liquid. (2) Cocks shall be ground to hold high 
vacuum. (3) Bores of cock keys shall meet outlets with precision. (4) 
The handles of keys shall be marked with colored glass to show positions of 
bores. (5) The handles of both keys shall be on the same side (front of 
drawing). (6) Vessel shall be carefully annealed. (7) Opening for no. 
rubber stopper shall be smooth and shall have standard taper of the stand- 
ard no. stopper. (8) Dimensions as given shall be followed as closely as 
possible. (9) No chipped keys or violation of the above specifications 
shall be accepted. 



HYDROGEN ELECTRODES 



183 



•iiiuimiiiiiiua 



=i 




L l hill im!|,.||i 



Q 
O 

K 

H 

O 

a 

a 
o 
M 



o 

S3 

3 



02 






184 THE DETERMINATION OF HYDROGEN IONS 

The electrode vessel is mounted in a clamp pivoted behind the 
rubber connection between J and H. This clamp runs in a groove 
of the eccentric I, the rotation of which rocks the vessel. In the 
manipulation of the vessel, the purpose is, first, to bring every 
portion of the solution into intimate contact with the electrode 
F and the hydrogen atmosphere, to make use of the principle of 
alternate exposure and immersion of electrode and then, when 
equilibrium is attained, to draw the solution into contact with 
concentrated KC1 solution and form a wide contact at H in a 
reproducible manner. The E. M. F. is measured directly after 
the formation of this liquid junction. 

The vessel is first flooded with an abundance of hydrogen by 
filling the vessel as full as possible with water, displacing this 
with the hydrogen, and then flushing with successive charges of 
hydrogen from the backed-up generator. Water or solution is 
run into the vessel from the reservoir D which can be emptied 
through the drain B by the proper turning of the cock C. Solu- 
tion or hydrogen displaced from the vessel is drained off at B'. 
These drains when they leave the electrical shielding (see p. 
231) should hang free of any laboratory drain. 

With the vessel rocked back to its lowest position the solution 
to be tested is run in from D (after a preliminary and thorough 
rinsing of the vessel with the solution) until the chamber E is about 
half full. Cock G is closed and cock C is turned so as to permit a 
constant pressure of hydrogen from A to bear upon the solution. 
For very careful work it is well to bubble hydrogen through the 
solution. The rocking is then commenced and is continued until 
experience shows that equilibrium is attained with the solution of 
the type under examination. The eccentric I should give the 
vessel an excursion which will alternately completely immerse the 
electrode F and expose it all to the hydrogen atmosphere. The 
rate of rocking may be adjusted to obtain the maximum mixing 
effect without churning. 

To establish the liquid junction the rubber tube between J and 
H is pinched while G is turned to allow KC1 solution to escape at 
B'. Then a turn of G and the release of the pinch draws the solu- 
tion down through the cock to form a broad mixed junction at H. 
For a new junction the old is flushed away with fresh KC1 from the 
reservoir N by properly setting cock L. 



HYDROGEN ELECTRODES 185 

With the closed form of calomel electrode, M, shown in the figure 
no closed stopcocks need be interposed between the terminals of 
the chain. With the customary calomel electrode vessel it is 
necessary to use a closed cock somewhere and since this must be 
left ungreased it is well to have it a special cock 1 at J. 

If a tube be led out from J and branched, several hydrogen 
electrode vessels may be joined into the system. At all events it 
is well to work with two vessels in parallel so that one may be 
flushing with hydrogen while the other is shaking. 

The electrode F is supported in a sulfur-free rubber stopper. 
A glass stopper may be ground into place but is seldom of any 
advantage and may prove to be a mistake. In the first place it 
is advisable to be free with electrodes and to instantly reject any 
which fail to receive a proper coating of metal. The inclination to 
do this is less if it entails the rejection of a carefully ground stop- 
per. Unless the stopper is accurately ground into place it is 
worthless. Furthermore it is very difficult to so grind a glass 
stopper that there will be left no capillary space to trap liquid. A 
rubber stopper can be forced into place without leaving such a 
space. The rapidity with which measurements are usually taken 
makes it improbable that a rubber stopper, if made sulfur free, 
can have any appreciable effect. If the rubber must be pro- 
tected a coating of paraffine will do. 

The calomel electrode M is of the saturated type so that no 
particular care need be taken to protect it from the saturated KC1 
used in making junctions. This is the working standard for the 
accurate standardization of which there is held in reserve the 
battery of accurately made, tenth-normal, calomel electrodes P. 
This battery may be connected with the system at any time by 
making liquid connection at and opening K. After a measure- 
ment the liquid junction is eliminated, the space rinsed with the 
tenth normal KC1, and liquid contact left broken. 

The design of this system is obviously for an air bath. The 
necessity of raising cocks out of an oil bath would not permit 
such direct connections as are here shown. 

1 To make an easily turning cock out of which KC1 will not creep, grease 
the narrow part of the socket and the wide part of the key. When the key 
is replaced there will be two bands of lubricant on which the key will ride 
with an uncontaminated zone between for the film of KC1 solution. 



186 THE DETERMINATION OF HYDROGEN IONS 




Fig. 20. Types of Hydrogen Electrode Vessels 

\ 



HYDROGEN ELECTRODES 187 

In figure 20 are shown several other designs of electrode vessels. 
A is one of the original Hasselbalch vessels which have since been 
modified for the use of replaceable electrodes. B (S0rensen), (Ellis) 
and C (Walpole), are operated in a manner similar to the vessel 
shown in figure 18. Walpole 's vessel was made of silica and the 
electrode was of platinum film as described on page 174. D (Mc- 
Clendon and Magoon) was designed for determinations with small 
quantities of blood. E (Michaelis) , employs a stationary hydrogen 
atmosphere and a wick connection for the liquid junction. G (Long) 
is a simple device which the designer thought applied the essential 
principles of Clark's vessel. Barendrecht 's vessel, H, is designed for 
immersion in an open beaker for estimations during titrations. 
It is similar to a design of Walpole 's (1914), but is provided with 
a plunger the working of which permits the rinsing of the bulb and 
the precise adjustment of the level of the liquid. Another immer- 
sion electrode is Hildebrand's, F, the successful operation of which 
depends upon a vigorous stream of hydrogen, which, on escaping 
from the bell surges the solution about the electrode. A modifi- 
cation which provides better protection of the electrode from 
oxygen is Bunker's design, I. 

At this point it may be of interest to note that Wilke (1913) at- 
tempted to make a hydrogen electrode by using a thin tube of pal- 
ladium on the interior of which hydrogen was maintained under 
pressure. One of the difficulties with such an electrode is the 
estimation of the hydrogen pressure at the solution-electrode in- 
terface. Wilke 's idea has never been developed to a practical 
point so far as we know, but it is worthy of study as an im- 
mersion electrode for industrial use. 

For titrations where exact control of liquid junction potential 
differences is of relatively less importance than control of wastage 
of the material titrated, the system illustrated in figure 21 is 
useful. Titrations are carried on in the Erlenmeyer flask 
which is held in place by the plate P. The arm carrying the 
spring may be attached to the support at A in a variety of ways. 
It may be bolted, riveted or screwed; but should be made with 
a "running fit" so that while held firmly, it may be turned to 
permit removal of the Erlenmeyer. The plate F should be rigidly 
attached to the support at B. In this plate there is turned a 
hole tapered to receive snugly the rubber stopper which holds 



188 



THE DETERMINATION OF HYDROGEN IONS 



the various attachments. If this hole is left rough from the lathe 



tne various attachments. 11 tms noie is leit rough trom the lathe 
tool the stopper will be held very firmly after the various glass 




Fig 21. A Hydrogen Electrode Vessel Suitable for Titrations 

tubes have been forced into place. ' The support has been illus- 
trated* in the drawing as if it were at the left. As a matter of fact 
it is behind the vessel, and carries at E a bar which supports the 



HYDROGEN ELECTRODES 189 

calomel cell K. The supporting system is illustrated roughly for 
there are various constructions which may be used. In the 
author's apparatus A is a screw connection and the junctions at B 
and E are riveted and soldered. 

It is of course essential that the solution be shaken after each 
step of the titration. If the support is clamped to a somewhat 
flexible rod the whole system may be shaken. Otherwise the 
glass vessel should be protected from the metal of the supporting 
plate by an inset of asbestos wood and then, if the spring is not 
too stiff, the vessel alone may be swirled. During a titration 
cock M is kept closed and N is left open. If the system is suffi- 
ciently rigid, if care is used in the operation of the cocks and if 
serious temperature changes are avoided very little of the solu- 
tion will be drawn into the capillary S and very little of the KC1 
will run or diffuse into the solution. 

A wire form of electrode will withstand shaking and possible 
scraping better than a foil electrode. 

Hydrogen is delivered beneath the surface of the liquid. At 
the first flushing an abundance of hydrogen is used; later but little 
is necessary. The hydrogen escapes through a tube not shown and 
should be run through a trap having a shallow layer of water. 

The burette tip shown in the figure is lengthened by a piece 
of capillary tubing. 

If the hydrogen be replaced by purified nitrogen and if the 
platinized electrode be replaced by a gold-plated electrode this 
vessel does very well for oxidation-reduction titrations. In this 
case the nitrogen is delivered above the solution and not below the 
surface. 

In some cases a preliminary reduction of a solution may be 
accomplished by making the solution, in the presence of hydrogen, 
travel down a long spiral of platinized wire. The spiral is made 
by winding no. 24 copper wire closely upon a rod, mounting it 
with a spread of the turns just sufficient to hold together descend- 
ing drops, plating with gold and then platinizing. Liquid de- 
livered slowly at the top of the spiral will be broken into drops 
which in the descent of the spiral are thoroughly stirred. The 
reduced solution is brought into contact with an electrode in a 
constricted part of the enclosing tube and is then delivere'd to a 
continuous-flow liquid junction such as that described by Lamb 



190 THE DETERMINATION OF HYDROGEN IONS 

and Larson or Maclnnes (see page 168). The hydrogen by suit- 
able devices may be given the carbon-dioxid partial pressure of 
the tested solution. Such a scheme is useful only in dealing with 
continuous treatment processes where abundance of material 
is available. 

Keller (1922) has described a hydrogen electrode with a re- 
placeable disk of platinum gauze. This is held by a cap to a hard 
rubber support which contains a portable calomel electrode. The 
system is rugged and may be used as an immersion chain for 
determining the pH values of liquids in commercial processes. 

In conclusion it may be said that with ordinary care almost any 
simple combination of electrode and electrode vessel will give 
fairly good results. On the other hand it is often necessary not 
only to provide against continuous loss of CO2 from biological 
solutions but also to arrange for rapid attainment of equilibrium. 
Since electrode measurements are often the last resort, since one 
can easily be misled by pseudo-equilibria and since attention to a 
few simple details of construction and operation frequently in- 
creases very greatly the speed of experimentation, the "simplicity" 
of certain designs is sometimes more apparent than real. 

However it would be invidious to select any particular design 
for criticism, the more so because none yet published is perfectly 
adapted to all purposes. Those described are therefore to be 
considered as illustrations from which the reader may select items 
or suggestions to incorporate in his own design. 

SUPPLEMENTARY REFERENCES 

Bailey (1920), Baker-Van Slyke (1918), Barendrecht (1915), Bose (1900), 
Bunker (1920), Dolezalek (1899), Eggert (1914-1915), Ellis (1916), 
Gooch-Burdick (1912), Clark (1915), Cullen (1922), Hasselbalch 
(1910-1913), Hastings (1921), Hildebrand (1913), Hudig-Sturm (1919), 
Konikoff (1913), Lewis-Brighton-Sebastian (1917), Linhart (1919), 
Long (,1916), Loomis-Acree (1911), Maloney (1921), McClendon (1915, 
1916, 1918), McClendon-Magoon (1916), Michaelis (1910, 1911, 1914), 
Michaelis-Rona (1909), Myers-Acree (1913), Peters (1914), Rudnick 
(1921), Sand-Law (1911), S0rensen (1909), Sturm (1918), Treadwell- 
Weiss (1920), Walpole (1913, 1914), Westhaver (1905), Wilke (1913). 



CHAPTER XIII 
Calomel Electrodes 

Unless otherwise specified the calomel electrode is an electrode 
in which mercury and calomel are overlaid with a definite concen- 
tration of 'potassium chloride. For particular purposes HC1 calo- 
mel electrodes or those containing some other chloride are used. 

The general type of construction is shown by A, fig. 23. A layer 
of very pure mercury is covered with a lajer of very pure calomel 
and over all is a solution of a definite concentration of KC1 satu- 
rated with calomel. 

The difference of potential between mercury and solution is 
determined primarily by the concentration of the mercurous ions 
supplied from the calomel. But, since there is equilibrium be- 
tween the calomel, the mercurous ions and the chlorine ions, the 
concentration of the mercurous ions is determined by the chlorine 
ion content furnished chiefly by the KC1. One of three concentra- 
tions of KC1 is usually employed — either 0.1 molecular, 1.0 molecu- 
lar or saturated KC1. These are ordinarily referred to as the 
"tenth normal-," "normal-" or "saturated calomel electrodes." 

The mercury used in the preparation of these electrodes or 
"half-cells" should be the purest obtainable. In Chapter XV 
methods of purification are described. Sufficient mercury should 
be used to cover the platinum contact deeply enough to prevent 
solution reaching this contact on accidental shaking. 

More portable half-cells are made by amalgamating a plati- 
num wire or foil. This is done by electrolyzing a solution of 
nercurous nitrate, the wire being the negative pole. Provision 
s then made for keeping a paste of calomel about this wire. 

Some success has been attained with the use of the better 
grades of calomel supplied on the market but the risk is so great 
hat it is best to prepare this material in the laboratory. A 
shemical and an electrolytic method will be described. 

The chemical 'preparation of calomel. Carefully redistill the best 
•btainable grade of nitric acid. Dilute this slightly and with it 
lissolve some of the mercury prepared as described in Chapter 

191 






192 THE DETERMINATION OF HYDROGEN IONS 

XV, always maintaining a large excess of mercury. Throw the 
solution into a large amount of distilled water making sure that 
the resulting solution is distinctly acid. Now, having distilled 
pure hydrochloric acid from a 20 per cent solution and taken the 
middle portion of the distillate, dilute and add it slowly to the 
mercurous nitrate solution with constant stirring. When the 
precipitate has collected, decant and treat with repeated quanti- 
ties of pure distilled water (preferably conductivity water). The 
calomel is sometimes washed, with suction upon a Buchner funnel 
but if due regard be taken for the inefficiency of washing by de- 
cantation it is preferable to wash repeatedly by decantation since 
there is thereby obtained a more even-grained calomel. Through- 
out the process there should be present some free mercury. 

Electrolytic preparation of calomel. Doubtless the better prepa- 
ration of calomel is formed by electrolysis according to the method 
of Lipscomb and Hulett (1916), This is carried out in the same 
way that the mercurous sulfate for Weston cells is formed. For 
the preparation of mercurous sulfate Wolff and Waters (1907) 
employ the apparatus shown in figure 22. An improvised appa- 
ratus may be made of a glass tube with paddles, platinum wire 
electrode and mercury contact and with two spools for bearing 
and pulley. In place of the sulfuric acid there is used normal 
hydrochloric acid. A direct current (from a four-volt storage 
battery) must be used. The alternating current sometimes used 
in the preparation of mercurous sulfate does not seem to work in 
the preparation of calomel according to some* preliminary experi- 
ments which Mr. McKelvy and Mr. Shoemaker of the Bureau of 
Standards kindly made for the writer. During the electrolysis the 
calomel formed at the mercury surface should be scraped off by 
the paddles c and c (fig. 22). The calomel formed by this process 
is heavily laden with finely divided mercury. 

Calomel formed by either the chemical or the electrolytic proc- 
ess should be shaken with repeated changes of the KC1 solution 
to be used in the half -cell before the calomel is placed in such a 
cell. 

The variations in the potentials of calomel electrodes have been 
the subject of numerous investigations. Richards (1897) ascribed 
it partly to the formation of mercuric chloride. Compare Rich- 
ards and Archibald (1902). Sauer (1904) on the other hand con- 



CALOMEL ELECTRODES 



193 



eluded that this had little to do with the inconstancy. Arguing 
upon the well known fact that the solubility of slightly soluble 
material is influenced by the size of the grains in the solid phase, 
Sauer thought to try the effect of varying the grain size of the calo- 
mel as well as the effect of the presence of finely divided mercury. 







Fig. 22. Wolff and Waters' Apparatus for the Electrolytic 
Preparation of Mercurous Sulfate or of Calomel 

With cells made up with various combinations he found the fol- 
lowing comparisons : 



Hg - calomel 


against 


calomel 


Hg+ = 


- 0.00287 volt 


(fine) (coarse) 




(fine) 


(coarse) 




Hg~ calomel 


against 


calomel 


Hg+ = 


- 0.00037 volt 


(fine) (coarse) 




(coarse) 


(coarse) 




Hg - calomel 


against 


calomel 


Hg+ - 


- 0.0025 volt 


(coarse) (coarse) 




(fine) 


(coarse) 





194 



THE DETERMINATION OF HYDROGEN IONS 




Fig. 23. Types of Calomel Electrode Vessels 



CALOMEL ELECTRODES 195 

Lewis and Sargent (1909) state that they do not confirm Sauer 
in regard to the effect of the finely divided mercury but that they 
do confirm him in regard to the state of the calomel. These au- 
thors and others recommend that grinding the calomel with mer- 
cury to form a paste be avoided as this tends to make an uneven 
grain. It is better to shake the mercury and the calomel together 
but this is unnecessary if electrolytic calomel is used. 

Here and there in the literature we find various other sugges- 
tions such as the elimination of oxygen from the cell ; but there 
seems to be no very substantial agreement in regard to this and 
several other matters as there is no substantial agreement in the 
preference of one concentration of KC1 over another. By the use 
of carefully prepared material and the selection of the better agree- 
ing members of a series, calomel electrodes may be reproduced to 
agree within 0.1 millivolt or better; but it has not yet been estab- 
lished whether or not this represents the order of agreement among 
electrodes made in different laboratories. Furthermore there 
still remains the question of the effect of minor disturbances. 
There is no question that "true" values are not to be expected 
until all parts of the system are in equilibrium and that a prelimin- 
ary shaking such as Ellis uses will hasten the attainment of equilib- 
rium. On the other hand a disturbance which will alter the 
surface structure of the mercury exposed may produce a slight 
temporary shift in the potential difference. The subject remains 
'or systematic investigation. 

The most extensive investigation of unsaturated calomel elec- 

rodes was made by Acree and his students (Myers and Acree, 

joomis and Acree), but how far the reproducibility which they 

ittained by short circuiting the differences of potential is repre- 

: entative of the general reproducibility of such electrodes is not 

; r et established. 

In figure 23 are shown several calomel electrode vessels each 
' rith a feature that may be adapted to a particular requirement. 
Valpole's (1914) vessel, A, is providedwith a contact that leads 
< ut of the thermostat liquid and with a three-way cock for flushing 
i way contaminated KC1. A more elaborate provision for the 
] rotection of the KC1 of the electrode is shown in the vessel of 
1 -ewis, Brighton and Sebastian (1917), B. A form useful as a sat- 
i rated calomel electrode in titrations is shown at C. Fresh KC1 



196 THE DETERMINATION OF HYDROGEN IONS 

passes through the U-tube to take the temperature of the bath 
and to become saturated with calomel shown at the bottom of 
this U-tube. D is Ellis' (1916) vessel, which in the particular 
form shown was designed to be sealed directly to the remainder of 
the apparatus used. A valuable feature is the manner of making 
electrical contact. Instead of the customary sealed-in platinum 
wire Ellis uses a mercury column. On closing the cocks the ves- 
sel may be shaken thoroughly to establish equihbrium. This 
feature has not been generally practiced. Vessel E is a simple 
form useful for the occasional comparison electrode. It may be 
made by sealing the cock of an ordinary absorption tube to a 
test tube and adding the side arm. F is the vessel of Fales and 
Vosburgh (1918) with electric contact made as in the familiar 
Ostwald vessel (G). 

In adding new KC1 solution to a vessel it must be borne in mind 
that the solution should be saturated with calomel before equihb- 
rium can be expected. It is well therefore to have in reserve a 
quantity of carefully prepared solution saturated with calomel. 

Lewis, Brighton and Sebastian (1917) state that certain grades 
of commercial KC1 are pure enough to be used in the preparation 
of KC1 solutions for the calomel electrode while other samples 
"contain an unknown impurity which has a surprisingly large 
effect upon the E. M. F. and which can only be eliminated by 
several recrystallizations. " It is therefore obvious that the only 
safe procedure, in lieu Of careful testing by actual construction of 
electrodes from different material, is to put the best available KC1 
through several recrystallizations. 

Acree has called attention to the possible concentration of the 
KC1 solution by the evaporation of water and its condensation on 
the walls of vessels unequally heated in thermostats. 

The values assigned to the potential differences at the several 
calomel electrodes at different temperatures vary. A judicious 
selection will wait upon the consideration of several important 
matters. Some of the more important of these will be presented 
in Chapter XIX. At this point however we may recount with- 
out comment some of the more frequently used values which the 
reader may choose to use. 

Clark and Lubs (1916) give the following compilation of Bjer- 
rum's values and those of S0rensen and Koefoed published by 
S0rensen (1912): 



CALOMEL ELECTRODES 



197 



TABLE 42 



Bjerrum 

S0rensen and Koefoed 
Bjerrum 



S0rensen and Koefoed. 



TEMPERATURE 



°c. 


18 
20 

25 

30 
40 
50 
60 
75 



POTENTIAL DIFFERENCE BE- 
TWEEN NORMAL HYDROGEN 
ELECTRODE AND N/10 CALOMEL 
ELECTRODE WHEN HYDROGEN 
PRESSURE IS 



Oneatmosphere 

less vapor 

pressure 



volts 

0.3366 

0.3377 
0.3375 

0.3367 

0.3364 
0.3349 
0.3326 
0.3290 
03243 



One 

atmosphere 



volts 

0.3367 

0.3380 
0.3378 

0.3371 

0.3370 
0.3359 
0.3344 
0.3321 
0.3315 



In the report of the "Potential Commission" of the Bunsen- 
Gesellschaft (Abegg, Auerbach and Luther, 1911) the normal hy- 
drogen electrode standard of difference of potential was adopted. 
This of course is only incidental except as temperature coefficients 
enter. The differences of potential between the normal hydrogen 
electrode and the tenth-normal and normal KC1 calomel electrodes 
were given as 0.337 and 0.284-0.283 respectively. .Auerbach 
(1912) in a review of this report called attention to the smaller 
temperature coefficient of the potential difference at the tenth- 
normal calomel electrode when referred to the normal hydrogen 
electrode (as having zero potential difference at all temperatures) 
and suggested that the tenth-normal electrode be taken as the 
working standard with the value 0.3370 between 20°C. and 30°C. 

Loomis and Acree (1911) present a choice of values for the 
tenth-normal calomel electrode at 25°C. referred to the normal 
hydrogen electrode. The choice depends upon the ionization as- 
cribed to the hydrochloric acid solutions used in their hydrogen 
electrodes and upon the values of the contact differences of poten- 
tial which were involved. Loomis (1915) i? inclined to accept the 
/alue 0.3360. 



198 THE DETERMINATION OF HYDROGEN IONS 

In 1914 Lewis and Randall applied " corrected degrees of dis- 
sociation" to the hydrochloric acid solutions used in arriving at 
the difference of potential at 25° between calomel electrodes and 
the theoretical normal hydrogen electrode. Denning the normal 
calomel electrode as the combination Hg Hg 2 Cl2, KC1 (1M), KC1 
(0.1 M) they reach the value 0.2776. The difference of potential 
between this electrode and the tenth normal they give as 0.0530. 
Whence the value for the tenth normal electrode is 0.3306. These 
values were revised by Lewis, Brighton and Sebastian (1917) 
to 0.2828 for the difference of potential between the normal 
calomel and the normal hydrogen electrode, and 0.0529 for the 
difference between the normal and the tenth normal. 

Beattie (1920) using more recent data calculates for the poten- 
tial difference at the normal calomel electrode 0.2826 and com- 
pares this value with 0.2824 which is Lewis, Brighton and Se- 
bastian's result (see above) when corrected by Beattie for the 
liquid junction potential difference between 0.1 N and 1 N KC1. 

It will have been noted that in measurements with the hydro- 
gen electrode there is no concern for the absolute difference of 
potential between mercury and solution. This is because the calo- 
mel half-cell is merely a convenient go-between for measurements 
in which one hydrogen electrode is compared with another. For 
this reason it is convenient to retain the "normal hydrogen elec- 
trode" standard of reference and it so happens that this is in 
harmony with a general though not universal custom adopted 
for all electrode measurements. 

Other systems are: first, that in which the difference of poten- 
tial between the mercury and a normal concentration of KC1 in 
a calomel electrode is taken arbitrarily as zero, and second that 
in which this difference of potential is given what is considered 
to be its actual value. 

Largely upon the basis of Palmaer's (1903) work the value 0.560 
volt has been used as the "absolute" difference of potential 
between mercury and N/1 KC1 saturated with calomel in the 
presence of solid calomel at 18°C. (The mercury being positive 
to the solution.) There is some skepticism 1 regarding the re- 

1 Whether this is just or unjust is a question concerning which we 
are in doubt. No critical review in the light of modern researches is known 
to the author. 



CALOMEL ELECTRODES 199 

liability of this value, but for the particular purpose with which 
we are now concerned it makes little difference what the value 
is if proper relative relations are maintained. But the difficulty 
in maintaining proper relative relations when there is no agree- 
ment on a standard basis of reference is made evident when we 
consider that the temperature coefficient for the absolute differ- 
ence of potential between mercury and solution is very different 
from the temperature coefficient for the difference of potential 
between calomel electrode and hydrogen electrode when the 
normal hydrogen electrode is defined as having zero potential 
difference at all temperatures. Thus, as shown by Fales and 
Mudge (1920), the absolute temperature coefficient of the satur- 
ated calomel half-cell is low and has a positive value. But the 
temperature coefficient of the values for the saturated calomel 
half-cell as used in hydrogen electrode work is negative and 
high. Fales and Mudge seem not to have made any independent 
measurements which furnish more reliable values for the differ- 
ence of potential between a saturated calomel half-cell and the 
"normal hydrogen electrode." These authors have however 
extended the work of Michaelis and have found evidence that 
the saturated calomel half-cell is reliable within the temperature 
interval 5°-60°C. 

As a working standard the saturated calomel half-cell is un- 
doubtedly the best as pointed out by Michaelis and Davidsohn 
(1912). It does not require careful protection from the saturated 
KC1 solution usually employed as a liquid junction and it has a 
high conductivity permitting full use of the sensitivity of a low- 
resistance galvanometer. It differs in no way from other calomel 
half-cells except that the solution is saturated with KC1 in the 
presence of solid KC1 at all temperatures used. 

There is not very good agreement between the values assigned 
bo the saturated calomel half-cell by different laboratories and it 
lad therefore best be regarded for the time being as a good work- 
ng-standard to be checked from time to time against carefully 
nade normal or tenth normal calomel electrodes or against a 
lydrogen electrode in a standard solution. For ordinary meas- 
urements however the values given in table a of the Appendix 
„re adequate. 



200 



THE DETERMINATION OF HYDROGEN IONS 



Michaelis (1914) gives the following table of values for the po- 
tential differences referred to the normal hydrogen electrode for 
the tenth normal and the saturated calomel electrodes. 



TABLE 43 



TEMPERATURE 


TENTH NORMAL 


SATURATED 


% 


15 




0.2525 




16 




0.2517 




17 




0.2509 




18 


0.3377 


0.2503 




19 




0.2495 




20 


0.3375 


0.2488 




21 




0.2482 




22 




2475 




23 




2468 




24 




2463 




25 




0.2458 




30 


0.3364 






37 




0.2355 




38 


0.3355 


0.2350 




40 


0.3349 






50 


0.3326 






60 


0.3290 







SUPPLEMENTARY REFERENCES 

Abegg (1902), Abegg-Auerbach-Luther (1909), Auerbach (1912), Bjerrum 
(1911), Bugarszky (1897), Clarke-Myers-Acree (1916), Coggeshall 
(1895), Coudres (1892), Ellis (1916), Fales-Vosburgh (1918), Lewis- 
Brighton-Sebastian (1917), Lewis-Sargent (1909), Lipscomb-Hulett 
(1916), Loomis (1915), Loomis-Aeree (1911), Loomis-Meacham (1916), 
Michaelis (1914), .Michaelis-David off (1912), Myers-Acree (1913), 
Newberry (1915), Palmaer (1907), Richards (1897), Richards-Archi- 
bald (1902), Sauer (1904), Steinwehr (1905). See also Chapter XIX 
for potential values. 



CHAPTER XIV 
The Potentiometer and Accessory Equipment 

The method usually employed in the measurement of potential 
differences is the Poggendorf compensation method, the poten- 
tiometer method. In principle it consists in balancing the poten- 
tial difference under measurement against an opposing, known 
potential difference. When the unknown is so balanced no cur- 
rent can flow from it through a current-indicating instrument such 
as a galvanometer. 

The principle may be illustrated by the arrangement shown in 
figure 24 which is suitable for very rough measurements. 

According to modern theory the conduction of electricity in 
metals is the flow of electrons, the electron being the unit electrical 
charge. By an unfortunate chance the two kinds of electricity, 
which were recognized when a glass rod was rubbed with silk, 
were given signs (+ for the glass and — for the silk) which now 
leave us in the predicament of habitually speaking of the flow of 
positive electricity when the evidence is for the flow of negative 
charges, the electrons. But so far as the illustration of principles 
is concerned it makes little difference and we shall depart from 
custom and shall deal with the negative charges in order to make 
free use of a helpful analogy. We may imagine the electrons, 
already free in the metal of our electrical conductors, to be com- 
parable with the molecules of a gas which if left to themselves 
will distribute themselves uniformly throughout their container 
(the connected metallic parts of our circuits). We may now im- 
agine the battery S (fig. 24) as a pump maintaining a flow of 
gas (electrons) through pipes (wires) to R to A to B and back to 
S. The pipe (wire) AB offers a uniform resistance to the flow 
so that there is a uniform fall of pressure (potential) from A to 
B while the pump (battery) S maintains a uniform flow of gas 
(electrons). If we lead in at C and at D the ends of the pipes 
'wires) from another pump (battery) X, taking care that the 
ligh pressure pipe (wire) from X leads in on the high pressure 
dde of AB, we can move C, D or both C and D until they span 

201 



202 



THE DETERMINATION OF HYDROGEN IONS 



a length of AB such that the difference of pressure (difference of 
potential) between C and D on AB is equal and opposite to the 
difference of pressure (difference of potential) exerted between 
C and D by X. Then no current can flow from X through the 
current-indicating instrument G and we thereby know that 
balance is attained. 

If we know the fall of electrical potential per unit length along 
AB the difference of potential exerted by X will be known from 
the length of wire between C and D. We now come to the man- 
ner in which this fall of potential per unit length is determined. 




I I I I I I I I i i I i i i 




Fig. 24. Elementary Potentiometer 

Choosing for units of electrical difference of potential, electrical 
resistance and electrical current, the volt, the ohm, and the am- 
pere respectively, we find that they are related by Ohm's law: 

,. N Difference in potential (in volts) 

Current (in amperes) = — — : ; : 

Resistance (in ohms) 



or 



R 



(41) 



With this relation we could establish the fall of potential along 
AB by measuring the resistance of AB and the current flowing. 
But this is unnecessary, for we have in the Weston cell a standard 



THE POTENTIOMETER 203 

of electromotive force (E. M. F.) which may be directly applied 
in the following manner. The unknown X (figure 24) is switched 
out of circuit and in its place is put a Weston cell of known E. M. F. 
Adjustment of C and D is made until the "null point" is attained, 
when the potential difference between the new positions of C and 
D is equal to the E. M. F. of the Weston cell. From such a setting 
the potential fall per unit length of AB is calculated. It must be 
especially noted however that for such a procedure to be valid the 
current in the potentiometer circuit must be kept constant between 
the operations of standardization and measurement for the fundamen- 
tal relationship upon which reliance is placed is that of Ohm's law 

E 

C = — . It will be noted that the establishment of the difference 
R 

of potential between any two points on AB by the action of S 
and the resistance of AB is strictly dependent upon the relation 
given by Ohm's law; but, since we draw no current from X when 
balance is attained, the resistance of its circuit is of no funda- 
mental importance. It only affects the current which can flow 
through the indicating instrument G when the potential differ- 
ences are out of balance. It is therefore concerned only in the 
sensitivity of G. 

The simple potentiometer system described above is susceptible 
to refinement both in precision and in convenience of operation. 

With the inevitable variations in the potentiometer current 
which occur as the battery runs down it would be necessary to 
recalculate from moment to moment the difference of potential 
per unit length of the wire AB if the procedure so far described 
were used. This trouble is at once eliminated if the contacts of 
the Weston cell can be thrown in at fixed points and the current 
be then adjusted by means of the rheostat R so that there is always 
the same uniform current producing, through the resistance be- 
tween the Weston cell contacts, the potential difference of this 
standard cell. Having thus arranged for the adjustment of a 
uniform current at all times and having the resistance of AB 
already fixed it is now permissible to calibrate the wire AB in 
terms of volts. 

In the Leeds and Northrup potentiometer (fig. 25), the resist- 
ance AB of our elementary instrument (fig. 24) is divided into two 
sections one of which A-D (fig. 25) is made up of a series of 



204 



THE DETERMINATION OF HYDROGEN IONS 



resistance coils between which M makes contact and the other 
portion of which is a resistance wire along which M' can slide. 
When the potentiometer current has been given the proper value, 
in the manner which will be described, the fall of potential across 
any one of the coils is 0.1 volt so that as M is shifted from the 
zero point D the potential difference between M and D is increased 
0.1 volt at each step. Likewise, when the current is in adjust- 
ment, the shifting of M' away from D increases by infinitesimal 
known fractions of a volt the difference of potential between M 
and M'. 




+O sc O- 



+ OEMfO- 



GA. O 



Fig. 25. Wiking op the Leeds and Northrup Potentiometer (Type K) 

Now to adjust the potentiometer current so that the several re- 
sistances in the potentiometer circuit will produce the differences 
of potential in terms of which the instrument is calibrated, use is 
made of the Weston cell in the following manner. By means of 
a switch, U, the unknown is thrown out and the Weston cell is 
thrown into circuit. One pole of the Weston cell circuit is fixed 
permanently. The other can be moved along a resistance at T 
constructed so that the dial indicates the value of the particular 
Weston cell in use. When so moved to agree with the particular 
cell in use, this contact at T is left in its position. Now the current 
flowing from the battery W is adjusted by means of the rheostat R 



THE POTENTIOMETER 



205 



until the difference of potential between T and 0.5 balances the 
potential difference of the Weston cell as indicated by the cessation 
of current in the galvanometer GA. The resistance T to "0.5" is 
such that the E. M. F. of the battery acting across this resistance 
will produce the desired potentiometer current. This current 
now acting across the several resistances furnishes the indicated 
potentials, i.e., a potential difference of 0.1 volt across each coil. 
Another arrangement which employs the ordinary sets of re- 
sistances in common use is illustrated in figure 27. 




Fig. 26. The Leeds and Northrtjp Potentiometer 

A and B are duplicate sets of resistances placed in series with 
the battery S. If the current be kept uniform throughout this 
system the potential difference across the terminals of B can be 
varied in accordance with Ohm's law by plugging in or out resist- 
ance in B. But to keep the current constant while the resistance in 
B is changed a like resistance is added to the circuit at A when it 
is removed from B, and removed from A when it is added to B. 

As mentioned before, the potential difference could be deter- 
mined from the resistance in B and a measurement of the current 
but this is avoided by the direct application of a Weston cell of 
known potential. Assuming constant current a Weston cell 
replaces X and adjustment to the null point is made by alter- 
ing the resistance in B with compensation in A. The unknown 
is then thrown into circuit and adjustment of resistance again 



206 



THE DETERMINATION OF HYDROGEN IONS 



made to the null point. If E w is the known E. M. F. of the Wes- 
ton cell, E x the potential of the measured cell, R w the resistance 
in circuit when the Weston cell is in balance and R c the resistance 
in circuit when the measured cell is in balance we have 



Whence 



C (constant) = — = — - 
R c Rv 



E x = 



E W R C 
Rw 



(42) 




Fig. 27. Elementary Resistance Box Potentiometer System 

The system is improved by providing means of regulating the 
potentiometer current till constant difference of potential is at- 
tained between terminals at which a Weston cell may be thrown 
into circuit. Then the resistances may be calibrated in volts. 

It will be noted that in this arrangement every switch or plug 
contact is in the potentiometer circuit. A bad contact, such as may 
be produced by failure to seat a plug firmly during the plugging 
in and out of resistance, or by corrosion of a plug or dial contact, 
will therefore seriously affect the accuracy of this potentiometer 
system. It requires constant care. 



THE POTENTIOMETEB 207 

Lewis, Brighton and Sebastian (1917) used two decade resist- 
ance boxes of 9999 ohms each. With an external resistance the 
current was adjusted to exactly 0.0001 ampere. Thus each ohm 
indicated by the resistance boxes when balance was attained cor- 
responded to 0.0001 volt. Their standard cell which gave at 25° 
1.0181 volts was spanned across B (fig. 27) and 182 ohms of the 
external resistance. 

Another mode of using the simple system illustrated in figure 
24 is a device frequently used by physicists, and introduced into 
hydrogen electrode work by Sand (1911) and again by Hilde- 
brand (1913). Instead of calibrating unit lengths along AD 
by means of the Weston cell, or otherwise applying the Weston 
cell directly in the system, the contacts C and D carry the terminals 
of a voltmeter. When balance is attained this voltmeter shows 
directly the difference of potential between C and D, and there- 
fore the E. M. F. of X. 1 

A diagram of such an arrangement is shown in figure 28. There 
is an apparent advantage in the fact that the Weston cell may be 
dispensed with and resistance values need not be known. There 
are however serious limitations to the precision of a voltmeter and 
in two cases which the author knows accuracy within the limited 
precision of the instruments was attained only after recalibration. 

A voltmeter is generally calibrated for potential differences 
imposed at the terminals of leads supplied with the instrument. 

Turning again to figure 24 we recall that when any given fall 
of potential occurs between A and B, a definite current flows in 
the circuit SRAB. If the resistance of AB is known a measure 
of the current flowing permits one to calculate the fall of potential 
between A and B. Thus a current-measuring instrument (am- 
meter) placed in series with the fixed resistance AB may be cali- 
brated to indicate differences of potential between A and B. 

1 It is sometimes assumed that because the circuit of the system under 
measurement is placed in the position of a shunt on the potentiometer cir- 
cuit that its resistance must be high in order that CD (fig. 24) may indicate 
correctly the potential difference. The fact that no current flows in this 
branch when balance obtains shows clearly that its resistance can have no 
effect on the accuracy of the indication. It has also been assumed that if 
CD is spanned by a voltmeter, the resistance of the voltmeter should be 
taken into consideration. But a voltmeter is calibrated to always indicate 
the potential difference between its terminals. 



208 



THE DETERMINATION OF HYDROGEN IONS 



To use this system the terminals of the gas chain C and D (fig. 
24) are moved to A and B and there permanently fixed. An 
ammeter is placed between R and S and adjustment of R is made 
until no current flows in G. The difference of potential between 
A and B as indicated by the calibrated and renamed reading of 
the ammeter is then equal to the E. M. F. of the gas chain. 

Much the same limitations noted in the voltmeter system apply 
to the ammeter system. 




Fig. 28. Voltmeter Potentiometer System 

A modification of the system briefly described above is found 
in the "Pyrovolter." The essential modification is a device of wir- 
ing whereby the same indicating instrument is used to measure 
current (indicated in volts) and to indicate the null point. 

In a few instances there has been employed a system of measure- 
ment, the principle of which is illustrated in the wiring diagram 
of figure 29. The E. M. F. of a gas chain is allowed to charge 
a fixed condenser c. By throwing the discharge key to the right 
the charge accumulated by the condenser is allowed to discharge 
through a ballistic galvanometer b, the deflection in which may be 
made a measure of the accumulated charge and hence of the 
E. M. F. of the gas chain. 



THE POTENTIOMETER 



209 



The ballistic galvanometer is one designed to indicate by the 
angular deflection of its coil the quantity of electricity passing 
through the coil as a sudden discharge. The quantity of elec- 
tricity stored in the condenser is a function of its dimensions 
and material and of the difference of potential imposed at its 



hEMFh 




■'ig. 29. Wiring Diagram Used in the Ballistic Galvanometer System 



erminals. The dimensions and material being fixed the charge 
■ecomes proportional to the difference of potential. Now a 
( efinite difference of potential may be imposed by means of the 
Veston cell w. The resulting charge in the condenser is discharged 
■ hrough the ballistic galvanometer giving the coil a definite 
( eflection. This serves to calibrate a given set-up if the galva- 
) ometer is so designed that the deflection at each section of the 



210 THE DETERMINATION OF HYDROGEN IONS 

scale is proportional to the quantity of electricity discharged 
through the coil and if the wiring be such that no serious changes 
of capacity and inductance occur in manipulation. 

The advantage of. this condenser method is that the condenser 
may be conveniently made of such capacity that insignificant 
current is drawn from the cell under measurement. If then the 
technique used at the electrodes is refined it should be possible 
to measure equilibrium potentials which would be easily dis- 
placed by current withdrawal. However, until there are pub- 
lished more definite data relating the conditions of electrode 
measurements to the theory of the condenser method, this system 
is not to be recommended for ordinary use. In a few instances 
when the potentiometer had already been ad j used to the potential 
of a gas chain the author has observed what appears to be an 
excessive E. M. F. unsupported by the equilibrium conditions 
under measurement. This disappears after an initial throw of the 
galvanometer and would not be apparent if the measurement were 
being made by adjusting the potentiometer from an original 
position sufficiently out of balance to permit a very sb'ght current 
to flow during successive taps of the key. Will such E. M. F/s, 
which are evidently temporary and do not represent the equilib- 
rium conditions under measurement, be recorded in the ballistic 
galvanometer method? 

Goode (1922) has used the 3-electrode vacuum valve in an 
arrangement for following the electromotive forces of gas chains. 

The 3-electrode electron tube is the instrument used as detec- 
tor and amplifier in radio-communication and is known by various 
names such as "the audion." A glass bulb (fig. 30) exhausted 
to a very low gas pressure is supplied with an atmosphere of elec- 
trons by their emission from the hot filament F. These electrons 
produce what may be called a space charge in the bulb. Surround- 
ing the filament is a metallic plate P which can be maintained at 
a potential about 22 volts more positive than the filament by 
means of the battery B. Under the influence of this fall of po- 
tential electrons migrate from filament to plate, producing the 
so-called plate-current. But interposed in this electron-drift 
is a grid, G, of wire or perforated sheet metal through which the 
electrons must pass in their migration from filament to plate. 
If this grid is charged positively with relation to the filament it 



THE POTENTIOMETER 



211 



will tend to neutralize the space charge and so assist the filament- 
to-plate current. Conversely, if the grid is charged negatively 
with relation to the filament, it will assist the space charge 
and so tend to oppose the filament-to-plate current. 

Thus the potential difference between filament and grid, a 
potential difference which may be impressed by a gas chain or 
other cell, can govern in large measure the filament-to-plate stream 
of electrons and a measure of this current can be made a measure 
of the E. M. F. of the cell, C. 



•I' H*£ 




Fig. 30. Wiring of Goode's System Employing the Electron Tube 

Goode considers the plate current I p to be made up of a con- 
stant current I Q characteristic of a given bulb and set working 
conditions and a current I p — I G which is a function of the poten- 
tial difference induced by C. To balance I Goode found that 
with the particular bulb he used it was sufficient to place a vari- 
able resistance R between the positive terminal of the A battery 
and the negative terminal of the B battery and to adjust this 
resistance till the galvanometer Ga was at its zero setting. Under 
these circumstances the deflection of Ga becomes a function of the 



212 THE DETERMINATION OF HYDROGEN IONS 

grid potential. Within the range of E. M. F. of the cells under 
study Goode found that with his particular apparatus the de- 
flection of Ga was a linear function of I P — I when Ga was shunted 
by a resistance r such that one large scale division corresponded 
to one unit of pH. 

Goode claims that the unique advantage of his system consists 
in the fact that so little current is drawn from the cell C that 
continuous readings may be made. This system should, there- 
fore, prove useful in studying those drifts of electrode potential 
which occur in a variety of cases and which need more thorough 
investigation. 

For the more refined uses to which Goode's system may be 
put it will be necessary either to know the characteristics of the 
bulb in use or else to carefully calibrate a given apparatus. 

The electron tube, when used as a valve for amplification, 
should be useful in making hydrogen electrode differences of 
potential control mechanical devices such as alkali or acid feeds 
for continuous commercial processes. 

NULL POINT INSTRUMENTS 

Referring to figure 24 and the accompanying text the reader will 
see that in the balancing of potential differences by the Poggen- 
dorf compensation method there is required a current indicating 
instrument to determine the null point. Such instruments will 
be briefly described, and some of their characteristics discussed. 

The galvanometer is a current-indicating instrument, which, in 
the form most useful for the purpose at hand, consists of a coil of 
wire in the magnetic field of a strong permanent magnet. This 
coil is connected into the circuit in which the presence or absence 
of current is to be detected. A current flowing through the turns 
of the suspended coil produces a magnetic field in its interaction 
with the field of the permanent magnet and tends to turn the coil 
so that it will embrace the maximum number of lines of force. 
The construction of galvanometers need not be discussed since it 
is a matter for instrument makers, but certain desirable qualities 
will be treated in a later section, together with the characteristics 
of other instruments. 

Provision should be made for the mounting of a galvanometer 



THE POTENTIOMETER 



213 



where it will receive the least vibration. If the building is sub- 
jected to troublesome vibrations some sort of rubber support 
may be interposed between the galvanometer mounting and the 
wall bracket or suspension. Three tennis balls held in place by 
depressions in a block of wood on which the galvanometer is 
placed may help. In some instances the more elaborate Julius 
suspension such as those advertised may be necessary. 




Fia. 31. A Galvanometer 

The capillary electrometer depends for its action upon the altera- 
ion of surface tension between mercury and sulfuric acid with 
.Iteration of the potential difference at the interface. A simple 
orm suitable for that degree of precision which does not call for 
he advantages of a galvanometer is illustrated in figure 32. 

Platinum contacts are sealed into two test tubes and the tubes 
j re joined as illustrated by means of a capillary K of about 1 mm. 
( iameter. In making the seals between capillary and tubes the 
( apillary is first blown out at each end and can then be treated as 
i tube of ordinary dimensions in making a T joint. After a thor- 



214 THE DETERMINATION OF HYDROGEN IONS 

ough cleaning the instrument is filled as illustrated with clean, dis- 
tilled mercury, sufficient mercury being poured into the left tube 
to bring the meniscus in the capillary near a convenient point. 
In the other tube is now placed a solution of sulfuric acid made 
by adding 5.8 cc. water to 10 cc. sulfuric acid of 1.84 specific 
gravity. The air is forced out of the capillary with mercury 
until a sharp contact between mercury and acid occurs in the 
capillary. The instrument is now mounted before a microscope 
using as high power lenses as the radius of the glass capillary will 
permit. The definition of the mercury meniscus is brought out 
by cementing to the capillary with Canada balsam a cover glass 
as illustrated. 

An important feature in the use of the capillary electrometer 
is its short circuiting between measurements. This is done by the 
key shown in figure 32. Tapping down on the key breaks the short- 
circuit and brings the terminals of the electrometer into circuit 
with the E. M. F. to be balanced. If the E. M. F. is out of bal- 
ance the potential difference at the mercury-acid interface causes 
the mercury to rise or fall in the capillary. Releasing the key 
short-circuits the terminals and allows the mercury to return to 
its normal position. Adjustment of the potentiometer is con- 
tinued till no movement of the mercury can be detected. To 
establish a point of reference from which to judge the movement 
of the mercury meniscus the microscope should contain the fa- 
miliar micrometer disk at the diaphragm of the eye piece. In 
lieu of this an extremely fine drawn thread of glass or a spider web 
may be held at the diaphragm of the eye piece by touches of Can- 
ada balsam. 

The quadrant electrometer is so little used as a null point instru- 
ment that only a brief description will be given. In the form 
useful for the purpose at hand a very light vane of aluminium is 
suspended by an extremely fine thread, preferably of quartz, 
which is metalized on the surface in order to conduct charges to 
the vane. The vane is surrounded by a flat, cylindrical metal 
box cut into quadrants. Two opposite quadrants are connected 
to one terminal and the remaining quadrants to another terminal. 
If now the vane or needle be charged from one terminal of a 
high-voltage battery the other terminal of which is grounded, 
and a difference of potential be established between the two sets 



THE POTENTIOMETER 



215 



of quadrants, the needle will be deflected by the electrostatic 
forces imposed and induced. When used as a null point instru- 
ment in connection with the potentiometer the two sets of quad- 
rants may be connected as are the terminals of the capillary 
electrometer and spanned by a short-circuiting key. 




Fig. 32. Diagram of Capillary Electrometer and Key 



Since the current drawn for its operation is only the amount 
lecessary to charge a system of very low capacity to the low po- 
ential difference when the potentiometer is slightly out of bal- 
ance with the measured E. M. F. (and to zero potential difference 



216 THE DETERMINATION OF HYDROGEN IONS 

at balance) the quadrant electrometer might be of special value 
in the study of easily displaced, electrode equilibria. However, 
the attainment of the desired sensitivity with some of these in- 
struments is a task requiring great skill and patience. Further- 
more the rated sensitivity is sometimes attained by adjusting the 
so-called electrostatic control to such a value that the zero posi- 
tion of the needle is rendered highly unstable. This combined 
with the very long period at high sensitivity renders the instru- 
ment unsatisfactory for common use. Against these objections 
are: first, the point mentioned above, and second the advantage 
that the instrument may ordinarily be left in circuit during the 
adjustment of the potentiometer as is not the case with the 
galvanometer. 

Telephone receiver. The modern high resistance telephone re- 
ceiver of the type used in radio reception may serve in an emer- 
gency [Kiplinger (1921)]. Lack of balance between potentiometer 
adjustment and measured E. M. F. is indicated by a click in the 
receiver when the potentiometer key is tapped; but there is of 
course nothing but the loudness of the click to show how far from 
balance the adjustment is, and only the decrement of the sound 
to indicate that adjustment in the proper direction is being made. 

Selection of null point indicators. In the selection of instru- 
ments for the measurement of the electromotive force of gas 
chains it is desirable that there should be a balancing of instru- 
mental characteristics and the selection of those best adapted to 
the order of accuracy required. A null point instrument of low 
sensitivity may annul the value of a well-designed, expensive and 
accurate potentiometer; and a galvanometer of excessive sensi- 
tivity may be very disconcerting to use. The potentiometer sys- 
tem and the null point instrument should be adapted one to the 
other and to their relation to the system to be measured. 

The several corrections which have to be found and applied to 
accurate measurements of hydrogen electrode potentials are 
matters of a millivolt or two and fractions thereof. Collectively 
they may amount to a value of the order of 5 millivolts. Whether 
or not such corrections are to be taken into account is a question 
the answer to which may be considered to determine whether a 
rough measuring system or an accurate one is to be used. For all 
"rough" measurements the capillary electrometer is a good null 



THE POTENTIOMETER 217 

point instrument. It has a very high resistance which hinders 
the displacement of electrode equilibria at unbalance of a crude 
potentiometer system. It is easily constructed by anyone with 
a knowledge of the elements of glass blowing, and without par- 
ticular care may be made sensitive to 0.001 volt. 

For "accurate" measurements there is little use in making an 
elaborate capillary electrometer or in temporizing with poor 
galvanometers. 

The apportionment of galvanometer characteristics is a compli- 
cated affair which must be left in the hands of instrument makers, 
but there are certain relations which should be fulfilled by an in- 
strument to be used for the purpose at hand, and general knowledge 
of these is quite necessary in selecting instruments from the wide 
and often confusing variety on the market. 

Galvanometer sensitivities are expressed in various ways. 
Since one's attention is centered upon detecting potential differences 
the temptation is to ask for the galvanometer sensitivity in terms 
)f microvolt sensitivity. There are two ways of expressing this 
vhich lead to different values. One is the deflection caused by a 
nicrovolt acting at the terminals of the galvanometer. The 
nore useful value is the deflection caused by a microvolt acting 
hrough the external critical damping resistance. But in the last 
analysis the instrument is to be used for the detection of very 
! mall currents and these currents when allowed to flow through the 
j ;alvanometer by the unbalancing of the circuit at a slight poten- 
lial difference are determined by the total resistance of the gal- 
vanometer circuit. The instrument might be such that a micro- 
volt at the terminals would cause a wide deflection, while, if 
1 Dreed to act through a large external resistance, this microvolt 
^ 'ould leave the galvanometer "dead. " For this reason it is best 
t d know the sensitivity in terms of the resistance through which a 
i nit voltage will cause a given deflection. This is the megohm 
sensitivity and is defined as "the number of megohms (million 
c hms) of resistance which must be placed in the galvanometer 
c rcuit in order that from an impressed E. M. F. of one volt there 
s lall result a deflection of one millimeter" upon a scale one 
r ieter from the reflecting mirror (Leeds and Northrup catalogue 
2 ), 1918). The numerical value of this megohm sensitivity also 
r ^presents the microampere sensitivity if this is defined as the 
e imber of millimeters deflection caused by one microampere. 



218 THE DETERMINATION OF HYDROGEN IONS 

In hydrogen electrode measurements the resistance of the cells 
varies greatly with design (length and width of liquid conductors) 
and with the composition of the solutions used (e.g. saturated or 
M/10 KC1). Constricted, long tubes may raise the resistance of 
a chain so high as to annul the sensitivity of a galvanometer unless 
this has a high megohm sensitivity. Dr. Klopsteg (private com- 
munication) states that the resistance of the galvanometer coil 
ideally should be of about the same order of magnitude as that 
of the cell to be measured if maximum sensitivity is to be gained. 
Here however we enter complexities, since the arrangements by 
which high megohm sensitivity is attained affect other galva- 
nometer characteristics. One of these, which is not essential but 
is desirable, is a short period. A short period facilitates the set- 
ting of a potentiometer. If the circuits are out of balance, as they 
generally are at the beginning of a measurement, the direction for 
readjustment may be inferred from the direction of galvanometer 
deflection without bringing the coil back each time to zero setting, 
but there comes a time when prompt return to zero setting is 
essential to make sure that slight resettings of the potentiometer 
are being made in the proper direction. 

For a return of the coil to zero without oscillation it is neces- 
sary to have some sort of damping. This is generally a shunt 
across the galvanometer terminals, the so-called critical damping 
resistance. This shunt permits a flow of current, when the main 
galvanometer circuit is opened, which is generated by the turning 
of the coil in the magnetic field. The magnetic field produced in 
the coil by this current interacting with the field of the perman- 
ent magnet tends to oppose the further swing of the coil. When 
the resistance of the shunt is so adjusted to the galvanometer 
characteristics that the swing progresses without undue delay to 
zero setting and there stops without oscillation, the galvanometer 
is said to be critically damped. Critical damping as applied to 
deflection on a closed circuit need not be considered when the 
galvanometer is used as a null point instrument. Since some of 
the best galvanometers are not supplied with a damping resist- 
ance the purchaser of an outfit for hydrogen electrode work should 
take care to see that he includes the proper unit. Underdamped 
and overdamped instruments will prove very troublesome or 
useless. 



THE POTENTIOMETER 219 

These very brief considerations are presented merely as an aid 
in the selection of instruments. The manner in which desirable 
qualities are combined is a matter of considerable complexity but 
fortunately makers are coming to appreciate the very simple but 
important requirements for hydrogen electrode work and are 
prepared to furnish them. The galvanometer now in use by the 
author has the following characteristics; coil resistance 530 ohms, 
critical damping resistance 9,000 ohms, period 6 seconds, sen- 
sitivity 2245 megohms. It is not the ideal instrument for the 
hydrogen electrode system in use but is satisfactory. A shorter 
period is desirable and a higher coil resistance to correspond 
better with the average resistance of the order of one to two 
thousand ohms in some gas chains, would be desirable; but im- 
provement in both of these directions at the same time may in- 
crease the expense of the instrument beyond the practical worth. 
Indeed certain instruments now on the market are satisfactory 
for almost any type of hydrogen electrode measurements. 

In using a galvanometer it is important to remember that while 
the E. M. F. of a cell is unbalanced its circuit should be left closed 
only long enough to show the direction of the galvanometer deflec- 
tion. Otherwise current will flow in one direction or the other 
through the chain and tend to upset the electrode equilibrium. 
A mere tap on the key which closes the galvanometer circuit is 
sufficient till balance is obtained. 

Of potentiometer characteristics little need be said for the choice 
in the first instance will lie between instruments sold by reliable 
makers. In the second instance the choice will lie between 
instruments of different range and many of the unique instruments 
may be at once eliminated by a calculation which shows that the 
reputed accuracy involves too close a scale reading to be reliable. 
Certain difficulties which enter into the construction of potentio- 
meters for accurate thermo-couple work are hardly significant 
for the order of accuracy required of hydrogen electrode work. 
The range from zero to 1.2 volts and the subdivisions 0.0001 
volt do for measurements of ordinary accuracy. There should 
be a variable resistance to accomodate the variations in individual 
Weston cells of from 1.0175 to 1.0194 volts, and provision for 
quickly and easily interchanging Weston cell with measured 
E. M. F. 



220 THE DETERMINATION OF HYDROGEN IONS 

Several of the features of standard potentiometers may be elim- 
inated without injury to their use for hydrogen electrode measure- 
ments and would reduce their cost. Steps in this direction have 
been taken by at least one manufacturer. 

Having described the fundamental principles of the potentio- 
meter it seems hardly worth while to discuss the numerous modi- 
fications found among manufactured instruments or used in the 
construction of home-made designs. With the advent into every 
town of the numerous and varied parts of radio apparatus cer- 
tain accessory parts of a potentiometer may be readily purchased 
and the amateur can concentrate his attention upon the essential 
resistances. But, unless he is equipped to make these with accur- 
acy and to mount them with care, he may waste the cost of a 
satisfactory instrument. 

With regard to the more special or unique designs found on 
the market it may simply be said that they were developed for 
special purposes and that unless these special purposes are to be 
accomodated, the purchaser will do well to depend only upon an 
instrument of universal applicability. 

When rubber is used as the insulating material of instruments 
employed as potentiometers the rubber should not be left exposed 
to the light unduly. The action of the light not only injures 
the appearance of the rubber but also may cause the formation 
of conducting surface layers. 

If the potentiometer system contains a sliding contact and 
this contact is not involved in the resistance of the primary poten- 
tiometer circuit proper, the contact should be kept heavily coated 
with pure vaseline. If there be any doubt whatever about the 
quality of this vaseline it should be boiled with several changes 
of distilled water, skimmed off when cool and then thoroughly 
dried. If this is done there will seldom be any need to resort to 
the heroic and dangerous procedure of polishing. 

It cannot be too strongly emphasized that while a low order 
of precision is often adequate for a certain purpose the employ- 
ment of crude measuring instruments often obscures the data of 
greatest significance. This statement should not be interpreted 
as a discouragement to those who are about to undertake measure- 
ments with some such system as that illustrated in figure 28 for 
important data have been obtained with just such instruments. 



THE POTENTIOMETER 221 

The statement is intended rather as an encouragement to the 
beginner who will find the handling of more precise instruments 
easy and the rewards rich. 

THE WESTON CELL 

The elementary construction of the Weston cell is shown in 
figure 33. The mercury in the left arm should be carefully puri- 
fied (page 239) and the same material should be used for the 
preparation of the cadmium amalgam. This amalgam consists 
of 12.5 per cent by weight of electrolytic cadmium. The amal- 
gam is formed by heating mercury over a steam bath and stirring 
in the cadmium. Any oxid formed may be strained off by pouring 
the molten amalgam through a test tube drawn out to a long 
capillary. 

Cadmium sulfate may be recrystallized as described by Wolff and 
Waters (1907). Dissolve in excess of water at 70°C, filter, add 
excess of basic cadmium sulfate and a few cubic centimeters of hy- 
drogen peroxid to oxidize ferrous iron, and heat several hours. 
Then filter, acidify slightly and evaporate to a small volume. Fil- 
ter hot and wash the crystals with cold water. Recrystallize 
slowly from an initially unsaturated solution. The cadmium sul- 
fate solution of a "normal" Weston cell is a solution saturated at 
whatever temperature the cell is used, and therefore the cell should 
contain crystals of the sulfate. The ordinary unsaturated cell 
has a cadmium sulfate solution that is saturated at about 4°C. 

In the study of Weston cells considerable attention has been 
paid to the quality of the mercurous sulfate. Perhaps the best 
and at the same time the most conveniently prepared material is 
that made electrolytically. Where the alternating current is 
available it is preferable to use it. A good average set of condi- 
tions is a sixty cycle alternating current sent through a 25 per cent 
sulfuric acid solution with a current density at the electrodes of 
5 to 10 amperes per square decimeter. With either the alternat- 
ing or direct current the apparatus described on page 192 is 
3onvenient. 

In the Weston cell the lead-in wires of platinum should be 
imalgamated electrolytically by making a wire the cathode in a 
solution of pure mercurous nitrate in dilute nitric acid. 



222 



THE DETERMINATION OF HYDROGEN IONS 



After filling the cell it may be sealed off in the blast flame or 
corked and sealed with wax. 

Since the preparation of a good Weston cell is a matter of con- 
siderable detail, since such cells must be properly and carefully 
made in order to establish the true potential differences in a poten- 
tiometer system, and since reliable cells of certified values may be 
purchased at a reasonable price, it hardly pays the individual 
investigator to construct his own. It would, however, be a con- 
venience if the materials could be purchased of the Bureau of 
Standards as was once proposed. 

In some portable Weston cells of commerce the mercury is 
introduced as amalgamated electrodes and the cadmium sulfate 
solution, instead of being always in the presence of cadmium 
sulfate crystals, is often saturated at about 4°C. Since this leaves 
the solution unsaturated at ordinary temperatures this cell is 




Hg z so7 

Hg 



mm 



CdSO. 





Hg-Cd 



• Fig. 33. Diagram of the Weston Standard Cell 

sometimes called the "unsaturated" type. The result is a cell 
having a much lower temperature coefficient than that of the 
"normal" cell. There remain, however, large, if opposite, tem- 
perature coefficients for the two arms; and it is therefore necessary 
to protect the cell from temperature changes which will affect 
the two arms unequally. Furthermore in all Weston cells there 
may be observed some degree of hysteresis and in particular 
cases this may be very marked. It is therefore advisable under 
all circumstances to protect any Weston cell from temperature 
fluctuations. 

Weston cells are standardized in terms of the international volt 
the secondary standard for which is the average E. M. F. of 



THE POTENTIOMETER 



223 



"normal" Weston cells maintained at each national standards 
laboratory. 

As the result of cooperative measurements by the national 
standards laboratories of England, France, Germany and the 
United States the value 1.01830 international volts at 20°C. was 
assigned to the "normal" Weston cell. The United States Bu- 
reau of Standards maintains a group of these normal Weston cells 
whose mean value is taken as 1.0183 international volts and serves 
for the standardization of the commercial cells. It is important 
to note that this international agreement came into force January 
1, 1911, and that prior to that time the values in force in different 
countries varied considerably. 

TABLE 44 



TEMPERATURE 


DIFFERENCE 


°c. 







+0.000,359 


5 


+0.000,366 


10 


+0.000,304 


15 


+0.000,179 


20 


0.000,000 


25 


-0.000,226 


30 


-0.000,492 


35 


-0.000,791 


40 


-0.001,114 



The temperature coefficient of the "normal" Weston cell is 
;iven by Wolff (1908) as: 

E t = Esq - 0.000,040,75 (t - 20) - 0.000,000,944 (t - 20) 2 + 
0.000,000,009,8 (t - 20) 3 (43) 

3y this formula the differences in volts from the 20° value are as 
;iven in table 44. 

In other words a normal Weston cell should have its certified 
/alue corrected by addition of the above corrections when used at 
emperatures other than 20°C. But an "unsaturated" Weston cell 
nay for all ordinary purposes be considered as having no tempera- 
ure coefficient and its certified value may therefore be used as 
; ;iven for all moderate variations from 20°C. The change in E. M. 
<\ of the unsaturated type is less than 0.000,01 volt per degree, 



224 THE DETERMINATION OF HYDROGEN IONS 

provided the precautions regarding temperature fluctuations 
previously mentioned are observed. 

While most commercial cells are of the "unsaturated" type, 
the purchaser should be informed whether a given cell is of the one 
type or the other. 

STORAGE BATTERIES 

The storage battery or- accumulator is a convenient and reli- 
able source of current for the potentiometer. Standard poten- 
tiometers are generally designed for use with a single cell which 
gives an E. M. F. of about two volts. 

The more familiar cell to which our attention shall be confined 
consists of two series of lead plates immersed in a sulfuric acid 
solution of definite specific gravity. The plates of one series are 
connected to one pole of the cell and the plates of the other series 
are connected to the other pole. When a current is passed through 
the cell it will produce lead peroxid upon the plates by which the 
positive current enters and spongy lead upon the other plates. On 
charging, therefore, the plates in connection with the positive pole 
assume the brown color of the oxid while the plates in connection 
with the negative pole assume the slate color of the spongy metal. 
The poles should be distinctly marked so that one need not inspect 
the plates to distinguish the polarity but should the marks become 
obscured and the cell be a closed cell the polarity should be care- 
fully tested with a voltmeter before attaching the charging cur- 
rent. In lieu of a voltmeter the polarity may be tested with a 
paper moistened with KI solution. On applying the terminals 
to the paper a brown stain is produced at the positive pole, — 
positive reaction at positive pole. 

In charging a cell the positive pole of the charging circuit should 
be connected to the positive terminal of the cell, else the cell will 
be ruined. If a direct current lighting circuit is available, it may 
be used to charge a cell, or battery of cells, provided sufficient 
resistance be placed in series. A 16-candle-power carbon filament 
on a 110-volt circuit allows about half an ampere to pass. A 
bank of 6 lamps in parallel will allow three amperes to pass if 
we neglect the battery resistance. Ordinarily one will do well 
to charge at a rate lower than that specified by the maker, for the 



THE POTENTIOMETER 225 

care of a battery consists chiefly in keeping the deposits even. 
Low rates of charge and discharge favor this. On charging, the 
voltage will rise rapidly to 2.35 volts where it will remain during 
the greater part of the period. When it rises to 2.5 volts the 
charging should be discontinued. It is when it has reached this 
voltage that the cell will "gas" vigorously. If a cell should fail 
to "gas" after a reasonable time it may have an internal short 
circuit due to warping of the plates or the scaling of conducting 
material. In searching for such a condition a wooden pry, never 
a metallic one, should be used. Careful handling and charging 
will generally prevent such short circuits. 

It is more economical to charge from a low voltage circuit but 
this is seldom available. Indeed there is often available only an 
alternating current of lighting-circuit voltage. To use the energy 
of an alternating current it must either be used with a motor 
generator furnishing a direct current (preferably of low voltage) 
or else rectified. There are now readily available a variety of 
rectifiers used in charging the batteries of radio amateurs. Most 
of these rectifiers when of the mechanical type are designed for 
charging a six-volt battery. If the operator of a hydrogen elec- 
trode has a two-volt cell for his potentiometer and a four-volt 
battery for operating the relay of the temperature control sys- 
tem he has a combination suited to the common and inexpensive 
type of rectifier. 

In the discharging of a cell the sulfuric acid is converted to sul- 
fate which is deposited. The result is the lowering of the specific 
gravity of the battery liquid. Thus the specific gravity of the 
liquid is highest when the battery is fully charged and lowers on 
discharging. If there be reason to suspect that the proper spe- 
cific gravity is not being maintained it should be measured with 
i hydrometer. Fresh sulfuric acid may be added if one follows 
carefully the specifications given by the manufacturer of the cell, 
'n making fresh solution only sulfuric acid free from metals other 
han lead, free from arsenic, and free from chloride and nitrate 
hould be used. There will be a continuous loss of water from the 
>attery liquid due to evaporation and gassing. This should be 
eplaced by distilled water during the recharging of the cell. 

In discharging a cell its voltage should not be allowed to fall 
1 elow 1.8 volts. When a cell has reached this voltage it should be 



226 THE DETERMINATION OF HYDROGEN IONS 

recharged immediately. If however the cell has been discharged 
to a lower voltage it should be recharged at half rate. 

In using a storage cell to supply potentiometer current it is es- 
sential that the highest stability in the current should be attained 
since the fundamental principle of the potentiometer involves the 
maintenance of constant current between the moment at which 
the Weston cell is balanced and the moment at which the measured 
E. M. F. is balanced. Steadiness of current is attained first by 
having a storage cell of sufficient capacity, and second by using it 
at the most favorable voltage. Capacity is attained by the num- 
ber and size of the plates. A cell of 60 ampere-hour capacity is 
sufficient for ordinary work. The current from a storage cell is 
steadiest when the voltage has fallen to 2 volts. When a potenti- 
ometer system of sufficient resistance is used it is good practice to 
leave the cell in circuit, replacing it or recharging it of course when 
the voltage has fallen to 1.8 or 1.9 volts, and thus insure the at- 
tainment of a steady current when measurements are to be made. 

In no case should a cell used for supplying potentiometer cur- 
rent be wired so that a throw of a switch will replace the discharg- 
ing with the charging circuit. The danger of leakage from the 
high potential circuit is too great a risk for the slight convenience. 



CHAPTER XV 

Hydrogen Generators, Wiring, Shielding, Temperature 
Control, Purification of Mercury 

Hydrogen generators. When there is no particular reason for 
attaining equilibrium rapidly at the electrode a moderate supply 
of hydrogen will do. When, however, speed is essential, or 
when there are used those immersion electrodes which are not 
well guarded against access of atmospheric oxygen an abundant 
supply of hydrogen is essential. Indeed it may be said that 
one of the most frequent faults of the cruder equipments is the 
failure to provide an adequate supply of pure hydrogen or the 
failure to use generously the available supply. 

Hydrogen generated from zinc and sulfuric acid has been used 

n a number of investigations. If this method be employed, 

particular care should be taken to eliminate from the generator 

;hose dead spaces which are frequently made the more obvious 

evidence of bad design, to have an abundant capacity with which 

o sweep out the gas spaces of cumbersome absorption vessels 

. md to properly purify the hydrogen. To purify hydrogen made 

irom zinc and sulphuric acid pass it in succession through KOH 

l olution, HgCl 2 solution, P2O5, red-hot, platinized asbestos, and a 

solution of Na 2 S 2 4 (See Franzen, Ber., 39, 906) (Henrich, Ber., 

k 8, 1915, p. 2006). 

A very convenient supply of hydrogen is the commercial, 
( ompressed gas in tanks. According to Moser (1920) the indus- 
t rial preparation varies but the chief methods are the electrolytic 
1 nd the Linde-Cara-Franck processes. Of these the first yields 
t le better product. Hydrogen by the second process contains 
s tnong other impurities, iron carbonyl which may be detected by 
t le yellow flame and the deposit of iron oxid formed when the 
r ydrogen flame impinges upon cold porcelain. Moser found that 
i' was impractical to remove this iron carbonyl and he states that 
h ydrogen containing it is unfit for laboratory purposes. On the 
;her hand, electrolytic hydrogen ordinarily contains only traces 
air and C0 2 and is free from arsenic and CO. To purify it 

227 



228 THE DETERMINATION OF HYDROGEN IONS 

pass the gas over KOH and then through a tube of red-hot, platin- 
ized asbestos. If it is desired to dry the hydrogen, use soda lime 
or P2O5, but not H2SO4 which is reduced. If P 2 B is used it should 
be free from P2O3, i.e., distilled in a current of hot dry air. 

In purchasing tank hydrogen it is well to be on guard against 
tanks which have been used for other gases. 

For controlling the flow of gas from a high pressure tank the 
valve on the tank itself is seldom sufficiently delicate. There 
should be coupled to it a delicate needle valve, if this can be 
obtained. If not there will be found on the market diaphragm 
valves for the reduction of the pressure. Even then there should 
be placed between the tank and the electrode vessel a T tube, one 
branch of which dips under mercury and forms a safety valve. 

Having metal connections to start with, it will be found very 
satisfactory to lead off with copper tubing, such as is used for 
automobile connections or specified as soft drawn, seamless copper 
tubing 4 mm. internal diameter and wall thickness 24 B. S. gauge. 
This can be soldered in the flame of a blast lamp, using borax for 
a flux, with a silver solder composed of 6.5 parts copper, 2.0 
parts zinc and 11.0 parts silver. This solder is described as fus- 
ing at about 983°C. A nickel wire is useful in spreading the 
flux and solder. 

On the whole electrolytic generators are more satisfactory if 
a direct current such as that of a lighting circuit is available. 
In figure 34 is shown a generator the body of which is an ordinary 
museum jar. The glass cover may be perforated by drilling with 
a brass tube fed with a mixture of carborundum and glycerine. If 
this mixture is kept in place by a ring paraffined in position, and 
the brass tube is turned on a drill press with intermittent 
contact of the drill with the glass, the perforation may be .made 
within a few minutes. The electrolyte used is ten per cent, 
sodium hydroxid. The electrodes are nickel. To remove 
the spatter of electrolyte and to protect the material in the heater 
the hydrogen passes over a layer of concentrated KOH solution; 
and to remove traces of residual oxygen the hydrogen is passed 
through a heater. In the design shown the gas passes through a 
tungsten filament lamp. Lewis, Brighton and Sebastian use a 
heated platinum wire. More commonly there is used a gas-heated 
or electrically heated tube containing platinized asbestos. In 



HYDROGEN GENERATORS, ETC. 



229 



the author's design shown in figure 34 the wiring is so arranged 
that when there is no demand for hydrogen the heater may be 
turned off at S2 and a lamp thrown into series with the generating 

- + 
I 




Fig. 34. An Electrolytic Hydrogen Generator 

circuit by switch Si. The generator then continues to operate 
on a low current and sufficient hydrogen is liberated to keep the 
system free from air. Such a generator can be run continuously 
for months at a time. When in use the generator carries about 



230 THE DETERMINATION OF HYDROGEN IONS 

4.5 amperes. If this current be taken from a high voltage light- 
ing system there must be placed in series a proper resistance which 
can be either built up by a bank of lamps or constructed from 
nichrome wire. 

Since rubber connections are often used in leading hydrogen 
it is of interest to note the following relative rates of diffusion of 
gases through rubber. 

Gab Rate 

Nitrogen 1.00 

Air 1.15 

Oxygen 2.56 

Hydrogen 5.50 

Carbon dioxid 13 .57 

Wiring. Whenever a set-up is to be made more than an improv- 
isation it pays to make a good job of the wiring. A poor connec- 
tion may be a source of endless trouble and unsystematized wiring 
may lead to confusion in the comparison of. calomel electrodes 
and the application of corrections of wrong sign. 

Soldered connections or stout binding posts that permit strong 
pressure without cutting of the wire are preferable to any other 
form of contact. If for any reason mercury contacts are used 
they had best be through platinum soldered to the copper lead. 
Copper wires led into mercury should not take the form of a 
siphon else some months after installation it may be found that 
the mercury has been siphoned off. 

Thermo-electromotive forces are seldom large enough to affect 
measurements of the order of accuracy with which we are now 
concerned if care be taken to make contacts so far as possible 
between copper and copper at points subject to fluctuations in 
temperature. 

A generous use of copper knife switches, can be made to con- 
tribute to the ease and certainty of check measurements. For 
instance if there be a battery of hydrogen electrodes and a set of 
calomel electrodes, wires may be led from each to a centre con- 
nection of single-pole, double-throw switches as shown in figure 35. 
All the upper connections of these switches are connected to the 
+ pole of the potentiometer's E. M. F. circuit, and all the lower 
connections to the — pole. By observing the rule that no two 
switches shall be closed in the same direction, short-circuiting of 



HYDROGEN GENERATORS, ETC. 



231 



combinations is avoided. The position of a switch shows at once 
the sign of its electrode in relation to any other that may be put 
into liquid junction. This is a great convenience in comparing 
calomel electrodes where one half-cell may be positive to another 
and negative to a third. Such a bank of single pole switches per- 
mits the comparison of any electrode with any other when liquid 
junction is established; and, if a leak occur in the electrical sys- 
tem the ability to connect one wire at a time with the potenti- 
ometer and galvanometer often helps in the tracing of the leak. 




Fig. 35. Switches for Connecting Half-Cells with Potentiometer 

Shielding. Electrical leaks from surrounding high potential cir- 
cuits are sometimes strangely absent from the most crude systems 
and sometimes persistently disconcerting if there is not efficient 
shielding. The principle of shielding is based on the following 
considerations. If between two supposedly well-insulated points 
on a light or heating circuit, or between one point of such a circuit 
and a grounding such as a water or drain pipe, there is a slight 
flow of current, the electrical charges will distribute themselves 
over the surface films of moisture on wood and glass-ware. At 
two points between which there is a difference of potential the wires 
of the measured or measuring system may pick up the difference of 
potential to the detriment of the measurement. If however all 
supports of the measured and measuring systems lie on a good con- 
ductor such as a sheet of metal, the electrical leakage from without 






232 THE DETERMINATION OP HYDROGEN IONS 

will distribute itself over an equipotential surface and no differ- 
ences of potential can be picked up. To shield efficiently, then, 
it is necessary that all parts of the system be mounted upon metal 
that can be brought into good conducting contact. In many in- 
stances the complications of hydrogen electrode apparatus and 
especially the separation of potentiometer from temperature bath 
make a simple shielding impracticable. Care must then be taken 
that all of the separate parts are well connected. Tinfoil winding 
of wire in contact with unshielded points can be soldered to stout 
wires for connection to other parts by dropping hot solder on the 
well-cleaned juncture. 

Shielding should not be considered as in any way taking the 
place of good insulation of the constituent parts of the measured 
or measuring systems. 

For further details in regard to shielding see W. P. White (1914). 

Temperature control is" a matter where individual preference holds 
sway. There are almost as many modifications of various types 
of regulators as there are workers. Even in the case of electrical 
measurements where orthodoxy interdicts the use of a water bath 
it has been said (Fales and Vosburgh) that it can be made to give 
satisfaction. 

Yet there are a few who may actually make use of a few words of 
suggestion regarding temperature control for hydrogen electrode 
work. 

As a rule the water bath is not used because of the difficulty of 
preventing electrical leakage. Some special grades of kerosene are 
sold to replace the water of an ordinary liquid bath but for most 
purposes ordinary kerosene does very well. The free acid some- 
times found in ordinary kerosene may injure fine metallic instru- 
ments. To avoid this use the grade sold as " acid-free, medium, 
government oil." 

A liquid bath has the advantage that the relatively high spe- 
cific heat of the liquid facilitates heat exchange and brings material 
rapidly to the controlled temperature, but compared with an air 
bath it has the disadvantage that stopcocks must be brought up out 
of the liquid to prevent the seepage of the oil. The advantage of 
the high specific heat of a liquid is falsely applied when the con- 
stancy of a liquid bath is considered to be a great advantage over 
the more inconstant air bath. The lower the specific heat of the 



HYDROGEN GENERATORS, ETC. 233 

fluid the less effect will variation in the temperature of that fluid 
have upon material which it is desired to keep at constant tem- 
perature. For this reason a well-stirred air bath whose tempera- 
ture may oscillate about a well-controlled mean may actually 
maintain a steadier temperature in the material under observa- 
tion than does a liquid bath which itself is more constant. It is 
the temperature of the material under observation and not the 
temperature of the bath which is of prime interest. 

An air bath can be made to give very good temperature control 
and since it is more cleanly than an oil bath and permits direct- 
ness and simplicity in the design of apparatus a brief description 
of one form used by the writer for some years may be of interest. 

A schematic longitudinal section illustrating the main features 
is shown in figure 36. 

The walls of the box are lined with cork board finished off on 
the interior with "compo board." The front is a hinged door 
constructed like the rest of the box but provided with a double 
glass window and three 4-inch hand holes through which appara- 
tus can be reached. On the interior are mounted the two shelves 
A and B extending from the front to the back wall and providing 
two flues for the air currents generated by the fan F. 

The writer at one time used a no. Sirocco fan manufactured 
by the American Blower Company, demounted from its casing 
and mounted in the bearing illustrated. He now uses a four- 
blade fan taken from a desk-fan and mounted so that it turns 
in the hole F of the partition and blows toward E. The baffle 
plates at E, made of strips of tin arranged as in an egg-box, 
and intended to establish parallel lines of flow when the centri- 
fugal fan was used, are now eliminated. 

In the illustration the oil cup is shown as if it delivers into an 
annular space cut out of the Babbit-metal bearing. In reality 
this annular space is provided by cutting away a portion of the 
steel shaft. 

The heating of the air is done electrically with the use of bare, 
aichrome wire of no. 30 B. and S. gauge. When using the centrif- 
ugal fan the wire is strung between rings of absestos board (the 
'lard variety known as "transite" or " asbestos wood") which fit 
:>ver the fan at H. With the blade-fan the partition at F is made 
)f asbestos board and the wire is strung over the opening. The 



234 



THE DETERMINATION OF HYDROGEN IONS 



air is thus heated at its position of highest velocity. The elec- 
trical current in this heating coil can be adjusted with the weather 
so that the time during which the regulator leaves the heat on is 
about as long as the time during which the regulator leaves the 
heat off. In other words adjustment is made so that the heating 
and cooling curves have about the same slope, or so that the heat- 
ing balances the loss of heat through the walls. 



1 FOOT 



t- i — r—\ — i — i i i i i 






— *—" 


-:— \ 

J 




E 


.^ 



Fig. 36. Cross Section of an Air Bath 

When the room temperature is not low enough to provide the 
necessary cooling the box I is filled with ice water. Surrounding 
this is an air chamber into which air is forced from the high pres- 
sure side of the fan. J should be provided with a damper which 
can easily be reached and adjusted. 

To lessen danger of electrical leakage over damp surfaces the 
air is kept dry by a pan of calcium chlorid. 

A double window at W over which is hung an electric light pro- 
vides illumination of the interior. A solution of a nickel salt is 
placed at this window to absorb the heat from the lamp. 



HYDROGEN GENERATORS, ETC. 235 

The double window in the door (not shown) should be beveled 
toward the interior to widen the range of vision. 

Such a box has been held for a period of eight hours with no 
change which could be detected by means of a tapped Beckmann 
thermometer and with momentary fluctuations of 0.003° as de- 
termined with a thermo-element. The average operation is a 
temperature control within ±0.03° with occasional unexplained 
variations which may reach 0.1°. Because of the slowness with 
which air brings material to its temperature the air bath is con- 
tinuously kept in operation, and if a measurement is to be made 
quickly the solution is preheated. 

Given efficient stirring and a considerate regulation of the 
current used in heating, accurate temperature control reduces to 
the careful construction of the regulator. For an air bath the 
ideal regulator should respond instantaneously. This implies 
rapid heat conduction. Regulators which provide this by having 
a metal container have been described but glass will ordinarily be 
used. At all events there are two simple principles of regulator 
construction the neglect of which may cause trouble or decrease 
sensitivity and attention to which improves greatly almost any 
type. The first is the protection of the mercury contact from the 
corroding effect of oxygen. The second is the elimination of plati- 
num contacts which mercury will sooner or later "wet," and the 
substitution of an iron, nickel or nichrome wire contact. 

After trials of various designs the author has adopted the two 
forms of regulator head shown in figure 37. 

For precise control at an inaccurately adjusted temperature 
form A is used. The platinum lead-in wire P is fused to the ni- 
chrome wire N. After filling the instrument with mercury, dry 
hydrogen is flushed through the head by way of the side tubes. 
These are then sealed off and serve as reservoirs for excess mer- 
cury. Adjustment is made by slightly overheating the body of 
the mercury, breaking off the capillary column by a tap of the 
hand and storing the detached portion in one of the side tubes. 
Such an adjustment is often troublesome when regulation at a 
particular temperature is desired; but, once the adjustment is made 
it is permanent, provided the contact wire is ground down to a 
fine thread so that it will not fill the capillary enough to cause the 
mercury thread to part on occasions of overheating. 



236 



THE DETERMINATION OF HYDROGEN IONS 



Form B permits delicate adjustment of the contact by means of 
the screw S but it requires skill to make such a head properly. 
The nichrome wire must fit very closely in the capillary R to pre- 
vent the wax and mercury seal at W from creeping downward. 
Such a close fit implies very careful glass blowing to maintain a 





Fig. 37. Thermo-Regtjlator Heads 

straight and unconstricted capillary. With the contact wire in 
place and the proper amount of mercury in the apparatus hydrogen 
is run in at T escaping through R. Then a bit of beeswax is 
melted about W and at the moment it hardens the hydrogen sup- 
ply is shut off, T is sealed, and then the wax is covered with a 
shallow layer of mercury. 



HYDROGEN GENERATORS, ETC. 237 

If the wire does not fit R with precision or if overheating occurs 
the mercury at W may find its way into the regulator head. It 
is much safer then, although it increases the difficulties of adjust- 
ment, to make the seal at W with DeKhotinsky cement. 

For an air bath it is best to seal such regulator heads to a 
grid of tubes. 

The permanency of regulators of such design when properly 
made is a great asset and well repays care in preparation. Regu- 
lators of each of these types have been in continuous operation for 
years without serious trouble. One of type A survived a severe 
laboratory fire and after readjustment operated well. 

Filling such regulators with mercury can be done most easily 
by first evacuating the vessel under some one of the various high 
vacuum pumps and then letting the mercury in slowly through one 
of the side arms drawn to a fine point which is. broken under 
mercury. 

A description of methods of purifying mercury will be found on 
page 239. 

For electrical control of temperature the scheme of wiring 
shown in figure 38 has proved satisfactory. 

Lamps which are neat, convenient, replacable forms of resist- 
ance, which are obtainable in variety and which indicate whether 
or not current is flowing are shown in figure 38 "by L. R is a 
resistance formed by a few turns of number 30 nichrome wire on 
Pyrex glass, porcelain or asbestos board. By shifting the brass 
contact clamp along this resistance the proper amount of cur- 
rent to operate the relay may be found by trial. Too strong a 
current is to be avoided. A sharp, positive action of the relay 
should be provided against the day when the relay contact may 
become clogged with dust. To reduce sparking at the regulator 
and at the relay contacts, inductive coils in the wiring should be 
avoided. Spanning the spark gaps with properly adjusted con- 
densers made of alternate layers of tin foil and paraffine paper 
may eliminate most of the sparking, if the proper capacity be 
used. For air regulation it is essential that the heater be of 
bare wire so that it cools the moment the current is turned off. 
Furthermore it is essential to adjust the current till the heating 
rate is close to the cooling rate of the air bath. For such control 
of the heating current there are inserted in series with the heater 



238 



THE DETERMINATION OF HYDROGEN IONS 



two lamp sockets in parallel permitting the insertion of either a 
fuse, one lamp or two lamps of various sizes. The other lamp 
shown in the heating circuit reduces sparking at the relay. 

For relay contacts the tungsten contacts used in gas engines 
are very good. 

Although methods of tapping an alternating current for the 
operation of a relay have been described it is safer to depend upon 
a battery. 




To 
VUa-YtY 



Fig. 38. Wibing for Temperature Control 

Purification of mercury. Pure mercury is essential for many 
purposes in hydrogen electrode work, — for the calomel and the 
mercury of calomel electrodes, for Weston cells should these be 
"home made," for thermo-regulators and for the capillary elec- 
trometer. 

The more commonly practiced methods of purification make use 
of the wide difference between mercury and its more troublesome 
impurities in what may be descriptively put as the "electrolytic 
solution tension." Exposed to any solution which tends to dis- 
solve base metals the mercury will give up its basic impurities 



HYDROGEN GENERATORS, ETC. 239 

before it goes into solution itself, provided of course the reaction 
is not too violent for the holding of equilibrium conditions. 

The most commonly used solvent for this purpose is slightly 
diluted nitric acid' although a variety of other solutions such as 
that of ferric iron may be used. 

To make such operations efficient it is necessary to expose as 
large a surface as possible to the solution. Therefore the mercury 
is sometimes sprayed into a long column of solution which is sup- 
ported by a narrow U-tube of mercury. The mercury as it col- 
lects in this U-tube separates from the solution and runs out into 
a receiver. To insure good separation the collecting tube should 
be widened where the mercury collects but this widening should 
not be so large as to prevent circulation of all the mercury. A 
piece of very fine-meshed silk tied over the widened tip of a funnel 
makes a fine spray if the silk be kept under the liquid. This sim- 
ple device can be made free from dead spaces so that all the mer- 
cury will pass through successive treatments. It is more difficult 
to eliminate these dead spaces in elaborate apparatus; but such 
apparatus, in which use is made of an air lift for circulating the 
mercury, makes practicable a large number of treatments. A 
combination of the air lift with other processes and. a review of 
similar methods has been described by Patten and Mains (1917). 

Hulett's (1905, 1911) method for the purification of mercury 
consists in distilling the mercury under diminished pressure in a 
current of air, the air oxidizing the base' metals. Any of these 
oxids which are carried over are filtered from the mercury by pass- 
ing it through a series of perforated filter papers or long fine cap- 
illaries. A convenient still for the purpose is made as follows. 
Fuse to the neck of a Pyrex Kjeldahl flask a tube about 30cm. long 
which raises out of the heat of the furnace the stopper that car- 
ries the capillary air-feed. Into the neck of the flask fuse by a T- 
joint seal a 1.5 cm. tube and bend this slightly upward for a 
length of 15 cm. so that spattered mercury may run back. To the 
end of this 15 cm. length join the condensing tube, which is simply 
an air condenser made of a meter length of narrow tubing bent 
zigzag. Pass the end of this through the stopper of a suc- 
tion flask and attach suction to the side tube of this flask. The 
mercury in the Kjeldahl flask may be heated by a gas flame or an 
electric furnace. For a 220 volt D. C. circuit 12 meters of no. 26 



240 THE DETERMINATION OF HYDROGEN IONS 

nichrome wire wound around a thin asbestos covering of a tin 
can makes a good improvised heating unit if well insulated with 
asbestos or alundum cement. A little of this cement applied 
between the turns of wire after winding will keep the wire in place 
after the expansion by the heat. 

In the construction of such stills it is best to avoid soft glass 
because of the danger of collapse on accidental over-heating. 
Hostetter and Sosman describe a quartz still. 

Both the air current, that is delivered under the surface of the 
mercury by means of a capillary tube, and the heating should be 
regulated so that distillation takes place smoothly. 

Since it is very difficult to remove the last traces of oxid from 
mercury prepared by Hulett's distillation the author always makes 
a final distillation in vacuo at low temperature. An old but good 
form of vacuum still is easily constructed by dropping from the 
ends of an inclined tube two capillary tubes somewhat over baro- 
metric length. One of these is turned up to join a mercury res- 
ervoir, the other, the condenser and delivery tube, is turned up 
about 4 inches to prevent loss of the mercury column with changes 
in external pressure. The apparatus is filled with mercury by suc- 
tion while it is inclined to the vertical. Releasing the suction and 
bringing the still to the vertical leaves the mercury in the still 
chamber supported by a column of mercury resting on atmospheric 
pressure and protected by the column in the capillary condenser. 
The heating unit is wire wound over asbestos. The heat should 
be regulated by a rheostat till the mercury distills very slowly. 
By having the mercury condense in a capillary the still becomes 
self-pumping. 

Perhaps few of us who work with mercury have a proper regard 
for the real sources of danger to health. The vapor pressure of 
mercury at laboratory temperatures is not to be feared, but emul- 
sification with the dust of the floor may subdivide the mercury 
until it can float in the air as a distinct menace. Its handling 
with fingers greasy with stop cock lubricant is also to be avoided 
on account of possible penetration of the skin but more particu- 
larly because of the demonstrated ease with which material on 
the hands reaches the mouth. 



HYDROGEN GENERATORS, ETC. 241 

REFERENCES 

Potentiometers 

Bartell (1917), Bovie (1915), Hildebrand (1913), Leeds and Northrup Cata- 
logue 70, McClendon (1915), Nye (1921), Sand-Law (1911), Slagle- 
Acree (1921), Wenner-Weibel (1914), White (1914), Will Corporation 
(1921). 

Galvanometers 

Leeds and Northrup Company Catalogue 20 (1918), White (1906). 

Capillary electrometer 

Boley (1902), Le Blanc (1890), Lippmann, G. (1875), Smith (1900) (1903). 

Quadrant electrometer 

Beattie (1910-12), Compton-Compton (1919), Dolezalek (1906). 

Weston standard cell 

Bureau Standards Circular 60, Report to International Committee (1912), 
Cohen-Moesveld (1920), Cohen-Walters (1920), Wolff (1908), Wolff- 
Waters (1907), Hulett (1906), Melon (1921), Oblata (1920). 

International electrical units 
Dellinger (1916), Bureau Standards Circulars Nos. 29, 60. 



CHAPTER XVI 

The Relation of Hydrogen Electrode Potentials to 
Reduction Potentials 

We must remember that we cannot get more out of the mathematical 
mill than we put into it, though we may get it in a form infinitely more 
useful for our purpose. — John Hopkinson 

As indicated in Chapter X the hydrogen electrode is but a 
special case of a general relation for the potential difference be- 
tween a metal and a solution. The hydrogen electrode is con- 
structed of a noble metal laden with hydrogen, and it may be 
asked what relation it bears to those electrodes which consist of 
the noble metal alone and which are used to determine the so- 
called oxidation-reduction potentials of solutions such as mix- 
tures of ferrous and ferric iron. 

If a platinum or gold electrode be placed in a mixture of fer- 
rous and ferric sulfate there will almost immediately be assumed 
a stable potential difference which is determined by the ratio 
of the ferrous to the ferric ions. The relation which is found to 
hold is given by the equation: 

fc-fc-MfcEsd (44) 

nF [Fern] 

where Eh is the observed potential difference between the elec- 
trode and the standard normal hydrogen electrode, E^ is a con- 
stant characteristic of this particular oxidation-reduction equilib- 

[Ferro] 
rium and equal to Eh when the ratio — — jj is unity, R, T, n 

and F have their customary significances, and [Ferroj and [Ferri] 
represent concentrations of the ferrous and the ferric ions re- 
spectively. This equation will be referred to later as Peters' 
equation. Its general form is: 

RT, [RED] , % 

where [RED] represents the concentration of the reductant and 
[OX] represents the concentration of the oxidant. 

242 



REDUCTION POTENTIALS 243 

If we plot Eh on one coordinate and the percentage reduction 
on the other coordinate, we obtain a set of curves identical in 
form for a given value of n. The position of each curve along 
the Eh axis is determined by the value of E k which fixes the middle 
point. Such a set of curves would present a picture comparable 
with that shown in figure 2. The picture, however, would be 
incomplete for reasons which will be given later. 

It will be clearly understood that in using the term oxidation 
or the term oxidant we do not imply that oxygen is concerned. 
Oxidation is one of those terms established under an old order 
of thought and carried on into a new order with its meaning 
broadened. In the transformation of ferrous to ferric iron by 
chlorine there is every reason to believe that the process is directly 
one of electron transfer; yet we speak of it as an "oxidation" 
because it was seen fit at one time to systematize such reactions 
in terms of the participation of oxygen. The counterpart of 
oxidation is reduction. This term does not directly indicate any 
relation to hydrogen, but it is often assumed that hydrogen is 
concerned in reduction in much the same way that oxygen was 
thought to be concerned in every "oxidation." 

Before coming to a more generalized theory we shall describe 
the relation between the hydrogen electrode and the oxidation- 
reduction electrode in terms of hydrogen and hydrogen ions. . 

It is known that certain reducing agents are so active that 
they evolve hydrogen from aqueous solutions. In such a solu- 
tion an electrode would become charged with hydrogen and 
would conduct itself much like a hydrogen electrode. The relations 
then obtaining can be extended and, if we wish to represent the 
interaction of the reducing agent with the hydrogen ions, we have: 

H + + reducing agent ^ H + oxidation product. 

If equilibrium is established for the above reaction 

[H+] [RED] = 
[H] [OX] 

[H] _ [RED] 

FH+] [OX] 



244 THE DETERMINATION OF HYDROGEN IONS 

[H] [RED] 

Substituting K zz^;, for the ratio "77^77 in Peters' equation 

(45) and placing n = 1 for the case at hand we have 

Since the atomic hydrogen bears a definite relation to the partial 
pressure of molecular hydrogen, P, through the equilibrium 

[Hj 2 = K h P 

we mav substitute, collect constants under another constant K', 
bring this under Ek and so obtain: 

- „, RT. \/~P~ , N 

E h = E k - — In _ .(46) 

Compare this with the general relation for the hydrogen electrode 

„ „ RT. V^P~ , % 

Eh = E H In — — (47) 

F [H + ] 

E H in (47) is zero by definition when there is used the "normal 
hydrogen electrode" system of reference. When (46) is placed 
on .the same basis E k is also zero, since each of the other terms in 

(46) is identical with the corresponding term in (47). 

In other words we have substituted for the oxidation-reduction 
equilibrium the corresponding point of equilibrium between 
hydrogen and hydrogen ions, and have considered the poten- 
tial difference at the electrode as if it were that of a hydrogen 
electrode. An inference is that wherever we have an oxidation- 
reduction equilibrium the components will interact with hydrogen 
ions (or water) liberating free hydrogen and building up in the 
electrode a definite pressure of hydrogen. Conversely, if hydro- 
gen is already present in the electrode at a pressure too high for 
the oxidation-reduction equilibrium in question, hydrogen will 
be withdrawn until its pressure is in harmony with the oxidation- 
reduction equilibrium (the position of the latter having been 
shifted more or less by the reduction) . When a constant pressure 
of hydrogen is maintained at the electrode, as it is in the customary 
use of the hydrogen electrode, no true equilibrium can be attained 



REDUCTION POTENTIALS 245 

until this hydrogen has so far reduced all the substances in 
the solution that they can support one atmosphere pressure of 
hvdrogen. 

Incidentally it may be mentioned that it is a matter of indiffer- 
ence whether we regard the reductant to interact with the hydro- 
gen ions or the oxidant with the hydroxyl ions or each with water. 
By use of the equilibrium equations which are involved we reach 
the same end-result whatever the path. And furthermore by 
the use of certain theoretical relations between the hydrogen elec- 
trode and the oxygen electrode we could define potential differences 
in terms of that of an oxygen electrode. 

This method of relating oxidation-reduction to electrode poten- 
tials is convenient for showing the condition which must obtain for 
a true hydrogen electrode potential; but when we attempt to 
follow some of the logical consequences of this, the customary 
exposition, we not only meet some serious difficulties but obscure 
some very important relations. 

Let us calculate the hydrogen pressure in equilibrium with an 
equimolecular mixture of ferrous and ferric chlorid in a solution 
held at pH 1. A platinum electrode in such a solution will have 
a potential about 0.75 volt more positive than the "normal hy- 
drogen electrode." Let us consider this to be the difference of 
potential between a hydrogen electrode at pH 1 and a normal 
hydrogen electrode. Let us calculate, then, the hydrogen pressure 
at 25°C. from the equation: 

0.75 = - 0.0599 log — 
0.1 

We find the hydrogen pressure to be about 10~ 27 atmospheres. 
At one atmosphere pressure a gram mol of hydrogen occupies 
about 22 litres and contains about 6 X 10 23 molecules. If the 
pressure is reduced to 6 X 10 -23 atmospheres there would be but 
one molecule of hydrogen in 22 litres. If reduced to 10 -27 at- 
mospheres there would be but one molecule in about 37,000 litres. 
To assume any physical significance in such values is, of course, 
ridiculous. 

It is only by courtesy then that an electrode in a mixture of 
ferrous and ferric iron at pH 1 can be considered as a hydrogen 
electrode. 



246 THE DETERMINATION OF HYDROGEN IONS 

This is but an instance of the physically absurd values encoun- 
tered when restricted points of view and restricted methods of expressing 
relations are applied to electrode potential differences. One or two 
other instances will be given to illustrate the fact that our 
present equations are incomplete in that they tell us little or 
nothing about the mechanisms at electrodes (see Langmuir 1916, 
also Smits and Aten 1916). 

Lehfeldt (1899) says of the so-called solution pressures postu- 
lated by Nernst and briefly discussed in Chapter X: 

we have Zinc 9.9 X 10 18 

Nickel 1.3 X 10° 

Palladium 1.5 X 10~ 36 

The first of them is startlingly large. The third is so small as to involve 
the rejection of the entire molecular theory of fluids. 

Lehfeldt then shows that, in order to permit at the electrode 
the pressure indicated above for palladium, the solution would 
have to be so dilute as to contain but one or two ions of palladium 
in a space the size of the earth. No stable equiHbrium could be 
measured under such a circumstance. On the other hand Leh- 
feldt calculates that to produce the high pressure indicated for 
zinc "1.27 grams of the metal would have to pass into the ionic 
form per square centimeter, which is obviously not the case." 
There is thus very good reason to refrain from attributing a limited 
and sometimes obviously untrue physical significance to the in- 
tegration constant in the fundamental equation for electrode 
potentials (see page 153). 

Another aspect of the matter was emphasized in a lively dis- 
cussion between Haber, Danneel, Bodlander and Abegg in Zeit- 
schrift fur Elektrochemie, 1904. Haber points out that, if the 
well established relation between silver ion concentration and the 
potential difference between a silver electrode and a solution 
containing silver ions be extrapolated to include the conditions 
found in a silver cyanide solution, the indicated concentration of 
the silver ion will be so low as to have no physical significance. 
Haber mentions the experiment of Bodlander and Eberlein where 
the potential and the quantity of solution were such that there 
was present at any moment less than one discrete silver ion. The 
greater part of the discussion centred upon the resolution of the 
equilibrium constant into a ratio of rates of reaction, and upon 



REDUCTION POTENTIALS 247 

the' conclusion that, if the silver ion in the cyanide solution has a 
concentration of the order of magnitude calculated, it must react 
with a speed greater than that of light or else that the known reac- 
tions of silver in cyanide solutions must take place partly with 
the silver complexes and not wholly with the silver ions. How- 
ever, we are now more directly concerned with another aspect of 
this interesting situation. The potentials observed in silver cya- 
nide solutions are well defined. We may choose to extend to 
such solutions the relation between the potential of a silver elec- 
trode and silver ion concentration. When we do, we find that the 
silver ion concentration by itself cannot account for the well-de- 
fined potential. How then is the stable and reproducible poten- 
tial supported? 

None of these discussions affect in any serious way those rela- 
tions for concentration chains which are founded upon thermo- 
dynamic reasoning provided it be remembered that the thermo- 
dynamic reasoning alone does not furnish any conception of the 
physical mechanisms of a process. The points mentioned do how- 
ever make it evident that values sometimes used are mere "cal- 
culation numbers" employed in a region of extrapolation where 
the actual physical significance is unknown. The inevitable con- 
clusion is that our equations are insufficiently generalized. 

Such "calculation numbers" as those mentioned in the pre- 
3eding discussion are often of very great usefulness, but lest 
ihey continue to obscure phenomena of significance we shall 
soon have to have equations more intimately related to the mech- 
misms as Langmuir pointed out in his 1916 paper. 

Now it will not remove the fundamental difficulty to use the 

reatment which follows; but this treatment may aid the student 

o retain an orderly view of important relations, and it will pro- 

" 'ide a basis from which to discuss the interrelations of electrodes 

<f different types. From this discussion a generalized point of 

" iew will be reached. 

It is generally agreed that the fundamental process in oxida- 
1 on-reduction is an exchange of electrons. A familiar example is: 

Ferric ion + electron ^=± ferrous ion 

Fe+++ + e ?± Fe++ 

Since such a reversible reaction is not dependent upon the 
F 'esence of an electrode (acting as a catalyst) it is probable that 



248 THE DETERMINATION OF HYDROGEN IONS 

an exchange of electrons is going on continuously. There must 
then be some condition virtually equivalent to a free-electron 
pressure. We may imagine a moment in the exchange during 
which the electron is balanced between the forces of each ion. 
At this moment the electron may be considered to belong to 
neither ion and to be a property of the environment. Undoubtedly 
the situation is not so simple as this picture suggests; and, al- 
though the presence of free electrons has been demonstrated in 
liquid ammonia and methylamine solutions, the experimental 
evidence is not sufficient to justify our assuming the presence of 
free electrons in aqueous solutions to be a fact. However, it may 
be said at once that we are not now concerned with the objective 
actuality. A pressure of free electrons is merely postulated as 
the virtual equivalent of a condition not yet clearly formulated; 
and it is to be used in much the same way that Nernst used "so- 
lution tension," destined from the first to be eliminated from 
those equations which are employed to formulate experimental 
data. 

Assuming then the presence of free electrons as representative 
of some condition which may be tentatively evaluated in terms of 
electron pressure, electron concentration, or electron activity, 
let us consider the electrons to obey the laws of an ideal solution, 
their concentration thus being amenable to the law of mass action. 

Then, for the equilibrium between ferrous and ferric ions we may 
write 

[Fe+++] [e] 

~pe^r =KFe 

Let the symbol [RED] stand for the concentration of a reduc- 
tant and [OX] for the concentration of the reductant's oxidation 
product. Then, in general, for the type of reaction represented 
below where n electrons are concerned we have the equilibrium 
equation (48) 

OX + ne^ RED 

[OX][e]" =K] (48) 



or 



[RED] 



M-V*^ 



REDUCTION POTENTIALS 249 

For the reaction 2H+ + 2e ^ H 2 the equilibrium equation is 

[H+] 2 r*i 2 



[H, 



= K H (50) 



In (50) [H2] refers to the concentration of molecular hydrogen 
in solution. Since we shall deal with the partial pressure of 
gaseous hydrogen, as is the custom, we introduce [H 2 ] = K P 
where K is the equilibrium constant and P is the partial pressure 
of gaseous hydrogen expressed in atmospheres. Collecting con- 
stants we have 

[H+Ne] 2 



= K H 



or 



[e] = ^K, 



P_ 

[H+] 2 



By the same procedure similar equations can be developed for 
any pair of oxidation-reduction products. 

We shall now introduce [e] into an equation formulating the 
difference of potential between an electrode and an aqueous solu- 
tion with which it is in contact. 

We shall assume the presence of free electrons in metals, as 
is commonly done. We have already postulated free electrons 
in solution as the virtual equivalent of the ability of the solution 
to give up electrons to a body brought into the solution. We 
shall now ascribe to the electrons in the metal phase and to the 
electrons in the solution phase activities £ m and £ s respectively, 
defining activity as Lewis has done (see page 278). 

The change in free energy accompanying the isothermal trans- 
fer of one Faraday of electrons from one phase to the other is 

AF = RTln^ 

If E is the difference of potential between metal and solution and 
F the Faraday, EF = A F 

Hence : E = — r In £ m — In £ s 

r r 






250 THE DETERMINATION OF HYDROGEN IONS 

More rigid equations of the same general form have been used 
by Herzfeld (1915, 1918), Langmuir (1916), Smits and Aten 
(1916), and Reichinstein (1921) and have been derived by reason- 
ing on kinetic as well as on thermodynamic theory. Certain 
aspects of the following treatment have been developed more 
fully by Smits and Aten. 

Now in the above equation we have used electron activity. 
In order to bring the further treatment into harmony with that 
used consistently throughout this book, we shall have to sacrifice 
a certain degree of generality and shall imagine that we are 
dealing with ver3>- dilute solutions wherein activity approaches 
concentration. The like assumption will be made for the activity 
of the electrons in the metal. Then we may write 

E = — In [e] m - — In [e], . (52) 

where [e] m is the concentration of electrons in metal and [e] B the 
concentration in the solution. 

Substitute for [e] 8 its equivalent in any one of the equilibrium 
equations and we have a result such as that given below. 

For instance, let two hydrogen electrodes be constructed of 
the same metal so that when these two electrodes 'are opposed 
as in a gas chain the Volta-effect between the electrodes and the 
copper of the measuring system will be compensated. The 
total E. M. F. of the gas chain is: 

VK H 
[H+] 2 
E.M.F. - — In e m - — - In [e] m -+ — In 
F F F 



V KH ii& 



If p = P' 



„.-„ RT, H+' 
E.M.F. = - — In ,- — f- 
F IH+] 

This is the simplest equation for a hydrogen electrode concentra- 
tion cell. In a similar way we obtain the equation for a con- 
centration cell of two "reduction potential" electrodes. 

It will be noted that in the case mentioned above the terms 
containing [e] m certainly cancel out. But will they if for one of 



REDUCTION POTENTIALS 251 

two like electrodes another of a different metal is substituted? 
Whatever the arguments for and against this may be, we believe 
that the electrochemical experimental data are quite insufficient to 
decide the question. Lest important phenomena be thus obscured, 
as Smits believes, the reader should be on his guard; but lest it 
be supposed that characteristic differences between different 
metals are thus eliminated it may be said at once that these 
differences will presently be found to be embodied in a complex 
of constants. We shall tentatively assume that the concentra- 
tions of the electrons in different metals are sufficiently alike 
to permit differences to be ignored for purposes of approximate 

treatment and shall regard the term — In [e] m as a constant, E m . 

r 

We then have a general equation for the difference of potential 

between any electrode and a solution of hypothetical electron 

concentration [e] s , namely, 

E = E m -^ln[e] s (53) 

To obtain an expression relating the potential difference at 
an electrode with the equilibria of the ions in solution it is now 
only necessary to write a given reaction in a form involving elec- 
tron concentration, to solve for [e] 8 and to introduce the equiva- 
lent of [e] 8 in equation (53). Thus the working equation is ob- 
tained by a uniform process, and, whatever the limitations 
of the development may be, it furnishes at one and the same time 
an easy method of remembering electrode relations and a view- 
point which helps to clarify the interrelationships of different 
systems. 

Since it will be convenient to refer all electrode potential differ- 
ences to that of the normal hydrogen electrode as the standard, 
the nature of the relation will be treated first. 

Combine equations (51) and (53) to give 



E = E m -^lnyK H 



But 



[m 



TD'T' 

——In vKh is a constant which we may call Eh. 



252 THE DETERMINATION OF HYDROGEN IONS 

Hence 

RT \/ P 
E = E m -E H -^ln^p (54) 

For an oxidation-reduction electrode we have from equations 
(49) and (53) 

E = E m -^lnK 1 ^PJ 
nF [OX] 

or, separating the new constant as we have done above, we have 

_ „ „ RT, [RED] , N 

E = Em _ El __ ln L__J (55) 

If now a normal hydrogen electrode and an oxidation-reduction 
electrode be opposed in a "chain" we have from (54) and (55) 
the full equation: 

E.M.F. = Em - E m + E H - E> + ^ln ^ - ^Inl^S 

F LH+] nF [OX] 

By definition E in equation (54) is zero when P and [H + ] are 
unity. Then E m — E H = 0. The above equation then (when 
one of the electrodes is the ".normal hydrogen electrode") re- 
duces to 

E .M.F. = E m - El -f,„^g! («> 

It will be noted that the constant in this equation (algebraic 
sum of E m and Ei) is not the simple constant of the oxidation- 
reduction equilibria, but is a complex. Furthermore the value 
is dependent upon the standard of reference used — in this case 
the normal hydrogen electrode. The complex nature of this con- 
stant has been discussed by Haber. 

It is customary to combine such constants as E m and Ei in the 
last equation. Furthermore it is convenient to maintain the 
same basis of reference, the normal hydrogen electrode. When 
this is done it shall be indicated by using for the electrode poten- 
tial the symbol E h . 

With these understandings we may at once write equations 
for several types of electrode-solution systems. 
For the hydrogen electrode 

Eh = _?T ln ^4: (57) 

F [H+l 



REDUCTION POTENTIALS 253 

For the oxygen electrode 

RT, [OH-] 
E h = E k0 -—ln-V-^ i (58) 

b VP02 
For an oxidation-reduction electrode 

F v _RT [RED] . . 

Eh - Ekl ^f ln ToxT (59) 

For a metal electrode in contact with solution containing metal 
ions of the electrode metal 

RT _[ML 

nF n [M n +] 



E h =E;-— ln^r (60) 



Here [M] 8 is the hypothetical concentration of metal in solution 
supposedly in equilibrium with the electrode. [M n+ ] is the con- 
centration of metal ions with n positive charges. 

If [M], = K[M] m , where [M] m is the concentration of undisso- 
ciated metal in the electrode and K is the equilibrium constant, 
We may substitute and collect constants thereby obtaining: 

Eh „ r _RT In [M] m 



nF [M n +] 

If the particular metal is always of the same density and state, 
and its electron concentration is constant (compare Smits), we 
can regard [M] m in the above equation as constant and so obtain 
equation (61) which is customarily used to relate the poten- 
tial difference at a given metal electrode to the concentration of 
the metal ions in the solution . 

E h = E M + ?£ In [M*+] (61) 

nF 

The potentials of amalgam electrodes may be derived in a com- 
parable way. 

In correlating all equilibria about the hypothetical electron 
concentrations of solutions, and connecting each in an electrode 
potential equation by means of equation (53) there is made evi- 
dent a definite interrelationship of all reactions involving elec- 
tron transfer. In the elementary development given, rigidity 
has been sacrificed for the sake of a simplicity which it is believed 
represents relations with sufficient truth to indicate the following 
important matters easily overlooked. 



254 THE DETERMINATION OF HYDROGEN IONS 

In the first place it is readily perceived that it is a mere matter 
of choice whether we regard a given electrode to be acting as an 
"oxidation-reduction electrode" or as a hydrogen electrode; 
and it only requires extension of the same principle to show that 
this same electrode can be considered as a metal electrode in 
equilibrium with a solution of its own ions. As indicated on 
page 245 a platinum electrode immersed in a solution of ferrous 
and ferfic ions if treated as a hydrogen electrode, furnishes a 
hydrogen pressure which can be considered only as a "calcula- 
tion value." By a similar procedure it can be shown that the 
estimated platinum-ion concentration would be a mere "calcula- 
tion value" so that we naturally avoid considering the electrode 
in this case as anything other than a means of picking up elec- 
trons in their transfer between Fe ++ and FC+++. 

Likewise a platinum electrode immersed in a solution may be 
said to function as an actual hydrogen electrode only when a 
finite concentration or pressure of hydrogen is known or provided. 
For such a pressure to be definite and stable the solution must 
be reduced to such an extent that any oxidation-reduction equi- 
librium in the solution is at a state compatible with the state of 
the equilibrium of the reaction: 

2H + + 2e ^ H 2 

which is under measurement. This is another way of stating 
the principle discussed on page 244. 

Another interesting relation is obtained by taking into consid- 
eration a certain hypothetical relation between the hydrogen 
electrode and the oxygen electrode. There are reasons for be- 
lieving that an oxy-hydrogen gas cell, i.e., a cell composed of a 
hydrogen and an oxygen electrode, each under one atmosphere 
of the respective gases should show an E.M.F. of 1.23 volts at 
all pH values. It is at once evident then that an oxygen elec- 
trode should enable one to measure pH values (see equation (58)), 
Or more directly pOH values. As a matter of fact the oxygen 
electrode" does not work well in practice and although Grube and 
Dulk (1918) believe that they have obtained experimental evi- 
dence for the theoretical relation between the oxygen electrode 
and the hydrogen electrode, the oxygen electrode is by no means 
a practical instrument. Why this is so has been a matter for 



REDUCTION POTENTIALS 255 

considerable debate. No satisfactory explanation has been of- 
fered. If, however, we assume the theoretical relations as a basis 
for argument, it is evident from what has already been said that 
we are privileged to express the relations between different 
electrodes in terms of an oxygen electrode. Likewise it is evident 
that to obtain an actual oxygen electrode potential it would be neces- 
sary to oxidize the material in solution to a point compatible with 
a definite and finite oxygen pressure. 

Leaving out all question of the numerical value of the oxy- 
hydrogen electrode and all question regarding the actuality of 
a hydrogen or oxygen pressure the genesis of equations (57) and 
(58) shows that a system can be defined in terms of either a hy- 
drogen electrode or an oxygen electrode. 

In the second place experimental data obtained with elec- 
trode measurements alone do not reveal the components which 
enter into the constant of an electrode potential equation. We 
shall presently deal with some relations between oxidation-reduc- 
tion potentials and the pH of the solution, and shall adopt for the 
sake of convenience the assumption that the reductant is an 
anion created from the oxidant by the introduction of one or more 
electrons. But the equations used to formulate the experimental 
data require only that proper relative relations be observed and 
it would be just as legitimate to consider the relation between 
oxidant and reductant from either of the following points of 
view: 

OX + 2e ^± RED 

OX + H 2 ^ hydrogenated reductant. 

The same form of electrode equation is obtained in either case 
and the decision between the two points of view is inextricably 
bound up in the complex nature of the constants which enter 
into the working equations. 

Thirdly, it is of great practical importance for many studies 
to note: that in any case where a definite potential difference is 
to be established at the electrode there must be in the system two 
species, one of which is the direct or indirect reduction product of 
the other, and that the ratio of their concentrations or activities 
must be of finite magnitude. Neglect of this principle is not 



256 THE DETERMINATION OF HYDROGEN IONS 

infrequent, and is doubtless due to the emphasis which has been 
placed upon the final, working form of the equation for the dif- 
ference of potential betw r een a metal and a solution of its ions. In 
obtaining the final form of this equation certain assumptions 
have been made and the potential difference at the electrode is 
made to appear as if it were dependent only upon the concentra- 
tion of one species, namely the metal ions. Whether this be 
the explanation or not, there are not infrequently encountered 
in the literature attempts to measure electrode potential differ- 
ences with a single oxidant or reductant. It should be plain 
from a study of figure 39 that, when the oxidant or reductant 
alone is present, the electrode potential difference becomes asymp- 
totic to the Eh axis. Were it possible to eliminate absolutely 
every trace of the oxidant, the potential difference obtained with 
the reductant alone would tend to become infinite. Wherever 
stable potentials have been reported as having been found with 
reductant alone it is doubtless due to the presence of the oxidant 
as an impurity. 

From the foregoing discussions it should be evident that the 
designation of a particular electrode-solution system depends so 
far as convenience is concerned upon relations which we seek, 
it being more convenient in some instances to formulate all data 
in terms of hydrogen electrode potentials and in other instances 
in terms of reduction potentials. So far as the actual physical 
maintenance of electrode conditions is concerned the designation 
of an electrode as of one or the other type will certainly depend 
upon a finite ratio of two products, one of which is the reduction 
product of the other; but the discovery of what these species 
are is often a most difficult problem for the solution of which the 
electrode equations by themselves are not sufficient. 

SOME ELEMENTARY RELATIONS OF HYDROGEN ION CONCENTRA- 
TIONS TO OBSERVED " REDUCTION" POTENTIALS 

In dealing with an oxidation-reduction equilibrium, as, for 
instance, that between ferrous and ferric iron, our first concern 
is with the relation between electrode potential difference and 
the ratio of the concentrations of the components added, or 
analytically determined. Now it is found that a given ratio of 
ferric arid ferrous salts does not give the same potential under 



REDUCTION POTENTIALS 257 

all circumstances as it should if we could substitute this fixed 
ratio in Peters' equation. It is convenient to assume that the 
true ratio to be substituted is the ratio of the ion concentrations 
and when this ratio can be found its substitution in Peters' equa- 
tion often yields a good constant. Alteration of the ion concen- 
tration from that of the total salt added may be due to incomplete 
ionization of the salt as added or to the withdrawal of ions by 
the formation of complexes. Very often the concentration of 
the active agents is determined by the concentration of the hydro- 
gen ions and it is with this that we are now concerned. 

To illustrate the problem let us assume that the active oxidant 
is neither acidic nor basic so that we can neglect any acidic or 
basic dissociation and in dilute solution identify the active con- 
centration [OX] with the total oxidant [S ]. Let us next assume 
that on reduction an electron is introduced into the body to 
make the reductant virtually acidic. The concentration of 
active reductant then becomes the concentration of the anion 
of an acid. [RED] must be identified as [RED], and, when there 
is sought the relation between observed potentials and total 
reductant and oxidant, use must be made of the equation for 

the acid dissociation : [RED] = — — I" r * where [SJ is the total 

concentration of reductant and K a is the acid dissociation con- 
stant for that particular seat of ionization concerned. Substitut- 
ing the above in equation (59) 



E h = E kl -^lnK a +^ 
nF nF 



lnT^-MH^l-— In^} 
L J nF [S ] 

or collecting constants 

E h = Ek+ H ln [ K . + [ H + ]]-?flng (62) 

In order to emphasize the effect of [H+] let us assume that the 

. [SJ . 
ratio — , is to be kept constant while [H+] is varied. Inspec- 
ts 

tion of (62) shows that while [H + ] is large in relation to K a , E h 

RT 

will vary as -^ In [H + ]. When [H + ] approaches and passes 

K a , variation of E h passes over gradually from the relation indi- 
cated above to the other extreme where there is no appreciable 
variation of potential with change in [H+], 



258 THE DETERMINATION OF HYDROGEN IONS 

Ordinarily these relations are not perceived because the varia- 
tion of [H + ] is insufficient, but the principle involved is to be 
found in the case of ferro-ferricyanide potentials as pointed out 
by Kolthoff, and they are more clearly to be perceived in the 
data on the oxidation-reduction potentials of certain dyes briefly 
reported by Clark (1920) and by Clark and coworkers (1921). 

Let us also consider the equilibria of the quinone-hydroqumone 
system. 

Quinone + 2d -ctrons ;=± anion of hydroquinone 
OC t H 4 + 2e^ OC 6 H 4 

If in equation (59) we identify [OX] as the total concentration 
of quinone, [S q ], then in the same equation [RED] must be iden- 
tified as the concentration of the divalent anion of hydroquinone 
[TT], and n = 2. 

*-*--wMw (63) 

If [S d ] is the total concentration of hydroquinone, [H 2 D] the 
undissociated hydroquinone, [HD] the first anion, [D] the second 
anion, Ki the first acid dissociation constant and K 2 the second 
acid dissociation constant we have: 

[hd] [h+] _ mm _ ~ 

~vm~ ~ "IhdT ~ ' 

and 

[S d ] = [H 2 D] + [HD] + [ D~] 

Solving the above equations for [ D ] and substituting in (63) we 
have: 



Eh-Efc-H lnKaK.+^ln 



[H+l'+KitH+J + KxK, 



] 



-— In ^3 (64) 

2F [SJ K } 

The second term can be combined with E kl to give E' k as will 
be done later. 

We shall consider only the order of magnitude of Ki and K 2 
and their combined influence. Scudder's tables give Ki = 
1 X 10" 10 . Let K 2 be assumed to be of the order 10 -11 . Neg- 



REDUCTION POTENTIALS 259 

lecting numbers of insignificant orders of magnitude we find that 
while [H + ] is large in relation to Ki and K2 (higher than 10~ 7 ) 

RT 

the third term in equation (64) reduces to + "^ In [H + ] 2 . 



Then 



0.000,198T [Sa] , x 

E h = E k - 0.000, 198TpH - £ log — j (65) 



Thus, if the ratio of total hydroquinone to total quinone be 
kept constant, the electrode potential difference, E h , is a linear 
function of pH within the limits of the assumptions made above. 
A departure from this relation should begin to appear near pH 
9, should become very marked at pH 10, and, if other phenomena 
could be ruled out, E h should no longer vary with pH when pH 
is larger than about 12 provided the magnitude of K2 has been 
correctly guessed. 

The experimental data to be mentioned in a later chapter indi- 
cate that the hydrogen pressure in equilibrium with an equimolec- 
ular mixture of quinone and hydroquinone is physically of an 
entirely negligible magnitude. 

As Biilmann has shown (see Chapter XX), a platinum electrode 
in the presence of a definite mixture of quinone and hydroquinone 
can be made to measure pH values. 

Besides cases of the type given above we have cases such as 
that of iron where the reaction 

Fe+++ + e ^± Fe++ 

is essentially the destruction by the electron of a point of basic 
ionization. 

It is also conceivable that the addition of two electrons may 
change an ampholyte to a diacidic compound. 

Available data are quite insufficient to show whether or not 
ionizations at points other than those immediately concerned 
in the oxidation-reduction process produce a marked effect upon 
the point actually concerned in the oxidation-reduction process. 
They probably do for any strain in the electronic forces at one point 
of a molecule must be felt to some extent at all other points. 

There may also be found cases where the electronic fields of 
force are so altered by the introduction of the electrons concerned 



260 THE DETERMINATION OF HYDROGEN IONS 

in reduction that the reductant, instead of becoming more acidic 
or less basic becomes less acidic or more basic. The system hemo- 
globin-oxyhemoglobin comes to mind; but the available data are 
altogether too meagre to permit a formulation of actual cases, 
or even to permit an appraisal of the present method of presenta- 
tion. We have only to keep in mind the fact that, if this method 
of treatment proves to be valuable, there may be found a wide 
variety of cases reducible to a form comparable with that of 
equation (62). There we find three terms. Of these the middle 
term is the one which will vary from case to case. It will con- 
tain [H + ] and the constants of the oxidation-reduction equilib- 
rium. This term will determine, not only the general form of the 
curve relating Eh to [H+], but also deviation or inflexion points 

fS 1 
when 7£~. and n are kept constant and [H+] is varied. 

Whenever the magnitudes of the equilibrium constants are in 

RT 

such relation to [H + ] that the middle term reduces to -^ In 

[H + ], as it may in (64), the electrode potential becomes a linear 
function of pH. Under these limited circumstances there can 
be calculated a hypothetical, constant, hydrogen pressure by the 
method given at the beginning of this chapter, — which pressure 
may be considered characteristic for the given equilibrium. Since 
such pressures are often of very small magnitude, and since they 
vary in magnitude even more than hydrogen ion concentrations, 
it is sometimes convenient to use a logarithmic system of no- 
tation similar to the pH of hydrogen electrode work and to let 

log — — = rH, where Ph 2 is the pressure of molecular hydrogen 

in atmospheres. 

Clark and coworkers have calculated rH values characteristic 
of various oxidation-reduction indicators. Examples are shown 
in table 45. 

As indicated above such rH values have a limited significance. 
Even near neutrality the indigo system departs from constant 
rH and in a manner indicated by a full equation comparable with 
(64). 

The manner in which the three variables — electrode potential, 
pH and percentage reduction, are related in certain cases is 
illustrated in figure 39. 



REDUCTION POTENTIALS 



261 



When it is desired to express the state of a solution without 
regard to any particular equilibrium it is best to return to the 
concept formulated in equation (53) as having the desired gener- 
ality. But lest terms such as electron concentration, pressure 
or activity gain an unwarranted appearance of reality through use, 
and lest numerical values connected with this concept be given 
meanings too arbitrary, it will be best to retain the use of the elec- 
trode potentials themselves and in general to call them reduction 
potentials. These specify with directness the general state of the 
solution. 





TABLE 45 






INDOPHENOL-INDOPHENOL WHITE 


TETRA SULFONATES OF INDIGO AND 
OF INDIGO WHITE 


pH 


rH 


pH 


rH 


4.36 


21.3 


3.09 


12.2 




5.33 


21.4 


4.51 


12.2 




6.64 


22.0 


5.90 • 


12.3 




7. DO 


21.4 
20.7 


6.48 


12.5 




8.98 






10.23 


20.5 


As pH increas 


;s rH increases 





Since a given mixture of oxidation and reduction products 
at a given pH stablizes the "reduction potential" of a solution, 
we have a condition comparable with the buffer action in the 
acid-base system. To distinguish stabilization of oxidation- 
reduction from acid-base buffer action we may use the term 
poising action. Thus a solution may be said to be poised at 
a given reduction potential when the addition or subtraction 
of oxidants or reductants does not seriously alter the reduction 
potential. 

For example in figure 39, if methylene blue at pH 4.6 is about 
75 per cent reduced we know that the reduction potential of the 
solution should be at about +0.1. If quite appreciable additions 
of oxidants or reductants do not displace the reduction potential 
very much from this point it is evident that the solution is " poised" 
at + 0.1. 

This brief outline will have indicated the profound importance 
of the hydrogen ion concentration of a solution for processes of 



262 



THE DETERMINATION OF HYDROGEN IONS 



oxidation-reduction. A striking demonstration is given in a 
lecture experiment by Stieglitz (1917, page 292). Formaldehyde 
in acid solution is comparatively inactive with silver ions. On 
alkalization of the mixture vigorous reduction of the silver occurs. 
It may also be shown that a proper mixture of ferro- and ferri- 
cyanid is inactive toward indophenol in neutral and alkaline 
solutions, that up to acidities of pH 4 the potential of the ferro- 
ferri mixture does not vary with pH while that of indophenol- 
indophenol white does. At acidities near pH 4 the two systems 
run into one another and the indophenol is reduced. 



100 



50 





I>vA.tc^O 


*l 


'fl 

•Wry/ 


7 

•ail 


A. 


(i 








I 


JJ 


J 


J 


\ \ 
J 





^f 



+.3 



+A 



-/ 



100' 



S<? 









rr 




r 


;' ;' 










4 


J 


V 




' i 


°m. B\vt 




J 


'J\ 




J 


J 


J 







+,* +.3 +.2. +•' ° -I -\ 

Fig. 39. Relation of pH to Oxidation-Reduction Equilibria of Indigo- 
Indigo White and Methylene Blue-Methylene White 

Abscissas: reduction potential. Ordinates: percentage reduction. Fig- 
ures on curves: pH values. 

Finally it may be said that all oxidation-reduction equilibria 
do not lend themselves equally well to potent iometric study. An 
enormous amount of experimental and theoretical investigation 
remains to be done. 

In passing, it may be mentioned that the instruments and many 
of the principles which have been here described for the determina- 
tion of hydrogen ion concentration are applicable in the deter- 



REDUCTION POTENTIALS 263 

mination of oxidation-reduction equilibria and in the titration of 
oxidizing or reducing substances. The oxidation-reduction elec- 
trode with potentiometric measurement has been applied exten- 
sively to the determination of the end points of titrations and to 
the -study of oxidation-reduction equilibria. 

While the effect of hydrogen ion concentration has been recog- 
nized in many of these studies altogether too little use has been 
made of the methods which have been applied in biochemistry 
for the control and measurement of pH. 



CHAPTER XVII 
Sources of Error in Electrometric^ Measurements of pH 

Besides faults in the potentiometric system there are a variety 
of sources of error which demand special attention. Some of 
these are specific to hydrogen electrode work; others are not. 

Sometimes the most trivial occurrence may cause considerable 
trouble; such is the bubble of gas that may persistently cling to 
the bore of a stopcock key which is part of a liquid connection. 
This is mentioned simply to emphasize the constant watchfulness 
required of the operator of a hydrogen electrode system. A well- 
shielded electrical system may be put out of commission in the 
most unexpected way. Miserly supply of hydrogen with which 
to sweep out hydrogen electrode vessels is perhaps one of the com- 
monest faults, but the hoarding of solutions which should be used 
to rinse away the buffer action of solutions previously used in a 
vessel may also be serious. 

Aside from such questions of technique there are certain inher- 
ent difficulties in the application of the hydrogen electrode method. 

We have already discussed in Chapter XVI the relation between 
the hydrogen electrode and the "reduction electrode," and have 
shown that no true hydrogen electrode potential can be attained 
until the solution is so far reduced that it can support one atmos- 
phere of hydrogen. It is thus made perfectly obvious that a meas- 
urement of pH must be preceded by a very thorough reduction 
of the solution. 1 

When we speak of reduction we mean reduction in its wide sense 
and include among the oxidizing agents those metal ions which 
at a given concentration may be reduced by one atmosphere of 
hydrogen. 

The hydrogen electrode if properly treated gives such a pre- 
cisely defined potential in certain well buffered inorganic solutions, 
reaches this potential so rapidly, returns when polarized, and 

1 In some instances it is important to remember that reduction of the 
constituents of a solution may so change the acidic or basic properties of 
these constituents that serious shifts in pH may occur. 

264 



ERRORS IN ELECTROMETRIC MEASUREMENTS 265 

adjusts itself to temperature and pressure changes so well that there 
is little doubt of its being a reversible, accommodating, relatively 
quick-acting electrode. It is perhaps because of this that it shows 
a hydrogen electrode potential in solutions which could be slowly 
reduced by hydrogen. For instance certain culture media may 
exhibit upon an electrode of platinum uncharged with hydrogen • 
a potential which is distinctly toward the oxidizing region of oxi- 
dation-reduction potential. That they are capable of reduction 
and that the first reduction potential is not a pseudo potential 
is shown by the orderly progress of the potential toward that of a 
hydrogen electrode under the activity of bacteria. Yet such 
culture media if treated in the first place as in making a hydro- 
gen electrode measurement exhibit a fairly constant and repro- 
ducible hydrogen electrode potential the calculated pH value 
from which checks well with colorimetric measurements. The 
explanation seems to be that although that complete reduction 
of material to a point where the oxidation-reduction equilibrium 
will support an atmosphere of hydrogen is not attained, there is 
established a virtual hydrogen electrode equilibrium by reason 
of the rapidity of action between hydrogen and hydrogen ion and 
the slowness of action between hydrogen and oxidizing agents. 

The effect of an intense oxidizing agent will be at once recognized. 
At the other extreme are the cases where no drift in the E. M. F. 
in the direction of an oxidizing action at the hydrogen electrode 
will be detected. Between these extremes lie the subtle uncer- 
tainties which make it advisable to check electrometric measure- 
ments with indicator measurements and to apply tests of repro- 
ducibility, of the effect of polarization, of the effect of time on 
drift of potential and all other means available to establish the 
reliability of an electrometric measurement in every doubtful case. 

There are effects of unknown cause which are included under 
the term "poisoned electrodes." An electrode may be "poisoned" 
by a well defined cause such as those to be mentioned presently; 
but occasionally an electrode will begin to fail for reasons which 
cannot be traced. There is hardly any way of putting an ob- 
server on his guard against this except to call his attention to the 
fact that if he is familiar with his galvanometer he will notice a 
peculiar drift when balancing E. M. F.'s. 

Arsenic deposits, adsorption of material by the platinum black 



266 THE DETERMINATION OF HYDROGEN IONS 

(with such avidity sometimes that redeposition of the black is 
necessary), the deposit of films of protein, have all been detected 
as definite causes of electrode "poisoning." Michaelis (1914) 
places free ammonia and hydrogen sulfid among the poisons. 
However, there is no special difficulty in obtaining hydrogen 
electrode potentials agreeing with colorimetric measurements in 
bacterial cultures containing distinct traces of ammonia or hydro- 
gen sulfid and apparently reliable measurements have been made 
of the pH values of ammonium-ammonium chloride mixtures. 
' Of the antiseptics used in biological solutions Michaelis (1914) 
states that neither chloroform nor toluol interfere if dissolved. 
He does not mention that chloroform may hydrolyze to hydro- 
chloric acid. Drops of toluol however affect the electrode. 
Phenol is permissible but of course in alkaline solutions partici- 
pates in the acid-base equilibria. 

There is an extensive literature upon the so-called "poisons" 
which interfere with the catalytic activity of the finely divided 
noble metals used on the hydrogen electrode. This literature is 
most suggestive, but there is still need for more direct studies of 
the conditions surrounding the catalytic activity of the hydrogen 
electrode. 

Simply for the sake of clearness we may distinguish two func- 
tions of the electrode. The electrode is first of all a convenient 
third body by which there is established electrical connection 
with the system hydrogen-hydrogen ions. That the equilibrium 
of this system should not be disturbed by the presence of a sub- 
stance "poisoning" the catalytic activity of the platinum black 
has been tacitly assumed in the derivation of the thermodynamic 
equation for electrode potential difference. If the reduction of 
the solution could be accomplished without dependence upon the 
catalytic activity of the electrode it should be theoretically possi- 
ble to attain a true hydrogen electrode potential even in the pres- 
ence of a "poison." However, in ordinary practice an electrode 
is used not only as an electrode per se but also as a hydrogenation 
catalyst. As such it is very sensitive to "poisons." "Poisons" 
are then to be regarded as the cause of sluggish electrodes. Among 
these we find all degrees. Hydrogenation to a point compatible 
with a true hydrogen electrode potential may be delayed but 
slightly and we may say that the electrode is a bit slow in attain- 
ing a stable potential without our ever suspecting a "poison;" 



« ERRORS IN ELECTROMETRIC MEASUREMENTS 267 

or the black metal may be so seriously injured that it becomes 
entirely impractical to await equilibrium. 

And just as " poisons" may render an electrode useless for practi- 
cal measurements, so the employment of accelerators of catalysis 
may promote efficiency. With the exception of a brief, unpublished 
note by Bovie little work has been done in this direction. 

From what has already been said the effect of the presence of 
oxygen is obvious. Indifferent gases such as nitrogen may be 
considered merely as diluents of the hydrogen and as such must 
be taken into consideration in accurate estimations of the partial 
pressure of hydrogen. Gases like carbon dioxid on the other 
hand act not only as diluents but also become components of 
any acid-base equilibrium established in their presence. 

In very many instances biological fluids contain carbonate and 
the double effect of the carbon dioxid upon the partial pressure 
of the hydrogen and upon the hydrogen ion equilibria render accu- 
rate measurements difficult unless both effects are taken into con- 
sideration and put under control. 

At high acidities in the neighborhood of pH 5 carbon dioxide 
will have relatively little effect upon a solution buffered by other 
than carbonates. As the pH of solutions increases the participa- 
tion of C0 2 in the acid-base equilibria becomes of more and more 
importance. The C0 2 partial pressure in equilibrium with the 
carbonates of a solution is a function of both the pH and the 
total carbonate. If, however, we consider for the sake of the 
argument that the total carbonate remains fairly low and constant, 
the C0 2 partial pressure becomes less with increase in pH while 
its effect upon the hydrogen ion equilibria increases with increase 
in pH. Therefore it may be said that it is of more importance 
under ordinary conditions to maintain the original C0 2 content 
of the solution than it is to be concerned about the effect of C0 2 
upon the partial pressure of the hydrogen. Furthermore the 
effect of diminishing the partial pressure of the hydrogen is of 
relatively small importance. 

For these reasons the bubbling of hydrogen through the solu- 
tion is to be avoided unless one cares to determine the partial 
pressure of C0 2 which must be introduced into the hydrogen to 
maintain the carbonate equilibria and then provides the proper 
mixture (Hober). The method usually employed is to use a vessel 
such as that of Hasselbalch, of McClendon or of Clark in which a 



268 THE DETERMINATION OF HYDROGEN IONS ♦ 

preliminary sample of the solution can be shaken to provide the 
solution's own partial pressure of C0 2 , and in which there is provi- 
sion for the introduction of a fresh sample with its full C0 2 pressure. 
The hydrogen supply is then kept at atmospheric pressure and 
the partial pressure of hydrogen in the electrode vessel is either 
considered to be unaffected by the C0 2 pressure or corrected from 
the known C0 2 pressure of the solution under examination. 

Of course in cases where the total carbonate in solution rises to 
considerable concentrations the partial C0 2 pressure may become 
of very significant magnitude and its effect in lowering the hydro- 
gen pressure must be carefully considered. 

In determining the hydrogen ion concentration of the blood by 
the electrometric method the two outstanding difficulties encoun- 
tered are the presence of carbonate and oxyhemoglobin. If hy- 
drogen is swept through the fluid it will remove so much of the 
C0 2 that the hydrogen ion concentration is lowered. If hydrogen 
is not swept through, the C0 2 will escape into the hydrogen at- 
mosphere about the electrode and reduce the partial pressure of 
the hydrogen. The oxygen present in the oxyhemoglobin "de- 
polarizes" the hydrogen' electrode and makes necessary the 
employment of the plasma. 

Evans (1921) has maintained that in the electrometric measure- 
ment of carbonate solutions the carbonate is reduced to formate 
and that for this reason previous measurements of the pH of 
blood have been in error. There are various theoretical reasons 
for doubting the validity of Evans' last conclusion; but since the 
question is one of fact Cullen and Hastings (1922) have investi- 
gated the matter and have failed to confirm Evans. 

The criterions of a good hydrogen electrode measurement are 
difficult to place upon a rigid basis but certain practical tests 
are easy to apply. Reproducibility of an E. M. F. with different 
electrodes and different vessels is the foremost test of reliability, 
but not a final test. Second is the stability of this E. M. F. when 
attained. It is not always practicable to distinguish between a 
drift due to alteration in the difference of potential at liquid 
junctions and a drift at the electrode but in most cases the drift 
at the liquid junction is less rapid and less extensive than a drift 
at the electrode when the latter is due to a failure to establish a 
true hydrogen-hydrogen ion equilibrium. A test which is some- 
times applied is to polarize the hydrogen electrode slightly and 



ERRORS IN ELECTROMETRIC MEASUREMENTS 269 

then see if the original E. M. F. is reestablished. This may. be 
done sufficiently well by displacing the E. M. F. balance in the 
potentiometer system. Where salt and protein errors do not in- 
terfere the gross reliability of a hydrogen electrode measurement 
may be tested colorimetrically. This checking of one system with 
the other is of inestimable value in some instances as it has proved 
to be in the study of soil extracts. There the possibilities of vari- 
ous factors interfering with any accurate measurement of hydrogen 
ion concentration dimmed the courage of investigators until Gil- 
lespie (1916) demonstrated substantial agreement between the 
two methods. Subsequent correlation of various phenomena 
with soil acidity so determined has now established the useful- 
ness of the methods. 

In addition to the tests so far mentioned there remains the test 
of orderly series. Certain of the general relations of electrolytes 
are so well established that, if a solution be titrated with acid or 
alkali and the resulting pH values measured, it will be known from 
the position and the shape of the "titration curve" whether the 
pH measurements are reasonable or not. This of course is a 
poor satisfaction if there is any reason to doubt the measurements 
in the first place but it is a procedure not be scorned. 

In dealing with protein solutions Robertson (1910) found that 
the electrode was injured by deposits of protein which he as- 
cribed to acid coagulation of the protein by the acid absorbed 
in the platinum black from previous measurements. Robertson 
therefore recommends that in a series of measurements with 
protein solutions the series be treated from the alkaline to the 
acid solutions. If his explanation be true there are instances 
where the reverse procedure should be followed. See sections 
on isoelectric points. 

Not infrequently the attempt is made to measure electrometri- 
cally the pH value of an unbuffered solution such as that of KC1. 
It is not entirely the fault of the method but rather of the nature 
of the solution that this is a task requiring the very highest 
refinements known to experimental art. If for the sake of the 
argument we assume that the solution under examination is that 
of a perfectly neutral salt having under ideal conditions a hydro- 
gen ion concentration of 0.000,000,1 N, a simple calculation will 
show what an enormous displacement in pH will be caused by 
the admittance of the slightest trace of CO2 from the atmosphere, 



270 THE DETERMINATION OF HYDROGEN IONS 

of alkali from a glass container, of impurities occluded in the 
electrode or of impurities carried into the solution with the sol- 
vent or solute. Conversely, even if the measurement were such 
as to give the true value under ideal conditions it would have 
little practical significance because of the difficulty in holding the 
conditions ideal. 

By the same reasoning it appears probable that it would be 
difficult to obtain true electrode potentials even with a potentio- 
metric system drawing no current during its adjustment. When 
no buffer is present there is a negligible reserve of hydrogen ions. 
But the introduction of the electrode with its enormous surface 
must displace the equilibrium. How much the displacement 
will be depends both on relative proportions of electrode and 
solution and on the technique used. 

The effect of temperature variations upon the accuracy of 
electrometric measurements is a question upon which it is difficult 
to pass judgment. Of course, if measurements are not intended 
to be refined one may assume the temperature of the room to be 
the temperature of the system at the moment of the electrical 
measurement. It is then a simple matter to select from tables 
the values and factors applicable at the selected temperature. 
Since such a procedure introduces errors which are not serious 
for many purposes the author's insistence upon temperature regu- 
lation has been criticized. Those who take this position are doubt- 
less able to escape the psychological effects of uncertainty, but 
they can hardly escape the inconvenience of having to deal with 
new values and new factors with every shift in temperature. 
Temperature control so simplifies rough measurements that much 
.time is saved, and for this reason is recommended even when it 
is unnecessary. But before the practice of neglecting tempera- 
ture control can have scientific standing it needs more experi- 
mental investigation than it has been accorded. Calculations 
are quite insufficient -for we have little data upon the hysteresis 
in the adaptation of different systems to temperature variation. 

Cullen (1922), finding that the temperature in an electrode 
vessel is seldom that of the surrounding air in a room subject to 
temperature variation, has devised a modification of the Clark 
electrode vessel whereby the temperature of the solution can be 
measured. The same modification can easily be made in a calo- 
mel electrode vessel. 



• CHAPTER XVIII 

Standard Solutions for Checking Hydrogen Electrode 

Measurements 

Id. the routine measurement of hydrogen ion concentrations it 
is desirable to frequently check the system. To do so in detail 
is a matter of considerable trouble ; but if a measurement be taken 
upon some solution of well defined pH, and it is found that the 
potential of the chain agrees with that determined by careful and 
detailed measurements upon all parts, it is reasonably certain 
that the several sources of E. M. F. are correct. 

Any one of the buffer mixtures whose pH value has been estab- 
lished may be used for this purpose, but there are sometimes 
good reasons for making a particular choice. 

S0rensen (1909) used a mixture of 8 volumes of standard gly- 
cocoll solution to 2 volumes of standard hydrochloric acid solution 
for the details in the preparation of which see page 109. Michaelis 
(1914) recommends what has come to be known as "standard ace- 
tate." This is a solution tenth molecular with respect to both 
sodium acetate and acetic acid. Its preparation and hydrogen 
electrode potential at 18°C. have been carefully studied by Wal- 
pole (1914). Walpole proposes two methods for its preparation: 

(1) From N-sodium hydroxid solution free from carbon dioxid and 
N-acetic acid adjusted by suitable titration (using phenolphthalein), so as 
to be exactly equivalent to it. 

(2) From N-sodium acetate and N-acetic acid adjusted by titration of 
a baryta solution, the strength of which is known exactly in terms of the 
N-hydrochloric acid solution used to standardize electrometrically the 
normal solution of sodium acetate . 

Walpole defines N-sodium acetate as a "solution of pure sodium 
acetate of such concentration that when 20 cc. are taken, mixed 
with 20 cc. of N-hydrochloric acid, and diluted to 100 cc. the 
potential of a hydrogen electrode in equilibrium with it is the same 
as that of a hydrogen electrode in equilibrium with a solution 0.2 
normal with respect to both acetic acid and sodium chloride." 
By mixing the N-acetate with the N-HC1 in accordance with this 

271 



272 



THE DETERMINATION OF HYDROGEN IONS 



definition and then determining the potential of a hydrogen elec- 
trode in equilibrium with it Walpole shows that the N-sodium 
acetate solution may be accurately standardized. In the fol- 
lowing table are given Walpole's values showing the relation of 



TABLE 46 



CUBIC CENTIMETERS OF N/1 HC1 TO 20 CUBIC 

CENTIMETERS N/1 NaAc DILUTED 

TO 100 CUBIC CENTIMETERS 


E. M. F. 


19.00 


0.5270 


19.40 


0.5155 


19.50 


0.5125 


19.90 


0.4945 


20.00 


0.4898 


20.39 


0.4712 


20.89 


4549 


21.00 


0.4525 



the E. M. F. of the chain: Hg | Hg 2 Cl 2 KC1 (0.1m) | KC1 (sat.) | Ace- 
tate | H 2 Pt at 18°, to the cubic centimeters of N-HCladdedto20cc. 
N-sodium acetate and diluted to 100 cc. If, for instance, the 

potential found is 0.4800 volts, the ratio 

Concentration of Na Ac 

Hence the sodium acetate is 0.9901N. 



is 



20.2 
20.0' 



These values are more convenient to use if plotted as Walpole 
has done. 



TABLE 47 



TEMPERATURE 


E. M. F. 


TEMPERATURE 


E. M. F. 


15 


0.5170 


21 


0.5180 


16 


0.5171 


22 


0.5183 


17 


0.5172 


23 


0.5186 


18 


0.5174 


24 


0.5190 


19 


0.5175 


25 


0.5195 


20 


0.5178 


34-38 


0.5200-0.5205 



Walpole found that the E. M. F. of the chain: Pt H 2 1 "standard 
acetate" |sat. KC1| 0.1m KC1 Hg 2 Cl 2 | Hg at 18°C. is 0.6046. The 
contact potential still to be eliminated was estimated by the 
Bjerrum extrapolation to be 0.0001 volt. Hence the true poten- 



STANDARDS FOR CHECKING 



273 



tial is 0.6045. This value seems to be the value of the chain 
corrected to one atmosphere hydrogen plus vapor pressure. 

Michaelis (1914) gives the values in table 47 for the difference of 
potential between the saturated KC1 calomel electrode and the 
hydrogen electrode in his standard acetate. 

It will be noted that both S0rensen's standard glycocoll and the 
standard acetate solutions must be constructed by adjustment of 
the components. While there is no great difficulty in this there 
remain the labor and the chance of error that are involved. Clark 



P H 



\ 








KHFhtkiUtc 













C.C. 



10 



Fig. 40. Titration of Phthalic Acid with KOH 



and Lubs (1916) have shown that acid potassium phthalate pos- 
sesses, a unique combination of qualities desirable for the standard 
under discussion. The first and second dissociation constants of 
phthalic acid are so close to one another that the second hydro- 
gen comes into play before the first is completely neutralized (see 
fig. 40). As a consequence the half-neutralized phthalic acid 
(KHPhthalate) exhibits a good buffer action. The salt of this 
composition crystallizes beautifully without water of crystalliza- 



274 



THE DETERMINATION OF HYDROGEN IONS 



* 



Pi 



tion, and, as was shown .by Dodge (1915) and confirmed by 
Hendrixson (1915) it is an excellent substance for the standard- 
ization of alkali solutions. As such it is used to standardize the 
alkali entering into the buffer mixtures of Clark and Lubs (see 
page 102) . The outstanding feature is that the ratio of acid to 
base is fixed by the composition of the crystals and not by ad- 
justment as in other standards. The salt may be dried at 105°C. 
and accurate concentrations constructed. The diffusion potential 
against saturated KC1 is somewhat higher than that of standard 
acetate as estimated by the Bjerrum extrapolation but not so 
high as to make good readings difficult. 
Clark and Lubs (1916) found for the chain: 

. HgHg 2 Cl 2 | KC1 (saturated) | M/20 KHPhthalate | H 2 Pt 

at 20°C. an E. M. F. of 0.4807 corrected to one atmosphere of 
. hydrogen. Their saturated calomel electrode was 0.0882 volt 
more negative than the average of a set of tenth normal calomel 
I electrodes. Assuming 0.3379 (cf. Chapter XIX) as the value of 
• the tenth normal calomel electrode and 0.0004 volt for the dif- 
fusion potential still to be eliminated, the hydrogen electrode 
potential of M/20 KHPhthalate at 20° is 0.2306. 

LJnfortunately the temperature relations of such chains are not 
accurately known. For ordinary work the pH of M/20 KHPhtha- 
late may be considered as 3.97 between 20° and 30°C. Assuming 
a liquid junction potential difference of 0.0004 volts we can reckon 
from these data the following total electromotive forces at various 
temperatures of the chain : 



Calomel electrode of KC1 cone. X 



Sat. KC1 



Hydrogen electrode 
at one atmosphere 
in KHPhthalate 



(i) 



STANDARDS FOR CHECKING 



275 



TABLE 48 





TOTAL E. M. F. 




X = 0.lM 


X=1.0m 


X=saturated KC1 
(approximate) 


18 
20 
22 
24 
26 
28 
30 


0.5675 
0.5689 
0.5704 
0.5719 
0.5733 
0.5748 
0.5763 


0.5158 
0.5170 
0.5181 
0.5192 
0.5204 
0.5215 
0.5227 


0.4800 
0.4802 
0.4806 
. 0.4812 
0.4817 
0.4822 
0.4827 



These values are entirely provisional ftfr temperatures other 
than 20°C. and require experimental verification before they can 
be used for precise standards. They are given as convenient 
standards for ordinary check measurements. 



CHAPTER XIX 
Standardization of pH Measurements 

In the development of the theory of electrolytic dissociation 
the hydrogen electrode came upon the scene comparatively late 
and after many of the quantitative relations had been established 
by conductance data. It was therefore natural that these data 
should have been accepted in the standardization of potentio- 
metric measurements. It now appears that the interpretation of 
conductance data is more complicated than at first supposed and 
that certain of the values that have been used in the standardiza- 
tion of potentiometric measurements are in doubt. The resulting 
confusion demands careful consideration. 

Let us review briefly the way in which conductance data enter 
into the potentiometric system. 

The following equation relates the potential difference, E, at 
a hydrogen electrode to the partial pressure, P, of hydrogen, the 
concentration of hydrogen ions, C, and the constant K, 

RT VP 
F c 

As shown in a previous chapter we are forced to one or an- 
other set of comparisons such as is found in a concentration cell 
where P and K are constant. In this case we have a measurable 
electromotive force and the relation 

RT d 
E. M. F. = ^rlnTT 

Thus we determine the ratio of two hydrogen ion concentra- 
tions if the solutions are sufficiently dilute to permit the applica- 
tion of the gas laws from which the above equation was derived. 
To apply this equation directly to the determination of either 
concentration Ci or C 2 the other concentration must be known. 
Conductance data have been relied upon to furnish the known 
concentration. 

Likewise, when a chain composed of a calomel electrode and a 

276 



STANDARDIZATION OF pH MEASUREMENTS 277 

hydrogen electrode is used, the value assigned to the calomel elec- 
trode is such that when it is subtracted from the total E. M. F. 
of tr?e chain the resulting E. M. F. is as if between a normal hy- 
drogen electrode and the hydrogen electrode under measurement. 
This implies the experimental determination of the difference of 
potential between a normal hydrogen electrode and the calomel 
electrode or else between the calomel electrode and a hydrogen 
electrode in some solution of known hydrogen ion concentration. 
To determine this known hydrogen i«n concentration conductance, 
data upon hydrochloric acid solutions have been relied upon. 

Unfortunately hydrochloric acid solutions exhibit the so-called 
anomalies of strong electrolytes which have already been mentioned. 
Although it was known from the first that hydrochloric acid solu- 
tions do not obey the dilution law , it was supposed that the ratio 
of the equivalent conductances at dilution v and at infinite dilution 
(where there is complete dissociation) would give the percentage 
ionization at dilution v and hence the hydrogen ion concentration 
at this dilution. However, this conclusion involves the assump- 
tion that the mobilities of the ions remain unaltered between 
dilution v and infinite dilution. Jahn (1900) and Lewis (1912) 
have questioned this assumption and within recent years the con- 
clusion has become firmly established among many investigators 
that the mobilities do change or else that the chemical activity of 
the ions of strong electrolytes is not strictly proportional to their 
concentration. In other words conductance data alone are not 
sufficient to define with precision the hydrogen ion concentrations 
of the hydrochloric acid solutions which have been used to stand- 
ardize the hydrogen electrode system of concentration chains. 
In support of this contention there have been brought forward 
comparisons of the concentration chains themselves. There is 

Ci 

evidence that the ratio — in the concentration chain formula 

is not necessarily determined with accuracy when a measurement 
of the E. M. F. of such a chain is taken. What is it then that is 
determined? The' way in which this question will be answered 
will doubtless form another interesting chapter in the philosophy 
of science. Focused upon this point are two tendencies; the one 
seeking to find the factors which interfere with the application of 
the simple gas laws so that the experimental data may be corrected 






278 THE DETERMINATION OF HYDROGEN IONS 

to apply to the "ideal;" the other seeking to formulate either the 
empirical data or the thermodynamic relations without special 
reference to the mechanisms involved. • 

It was an astute suggestion of Lewis (1907) that the simple 
thermodynamic relations be assumed to hold, not for concentra- 
tion pressure relations, but for quantities which, when introduced 
into the equations embodjdng the gas laws, will make these laws 
apply. The two new quantities are activity and fugacity. In the 
special case of a "perfect" solution, a very dilute solution, obeying 
the laws of gases, activity and fugacity are equal to concentration 
and pressure respectively. But when a solute ceases to conduct 
itself in accord with the laws of gases, its fugacity and activity 
remain such that the equations which apply to "perfect" solutions 
still hold. 

Stated in the above manner it may appear to those who insist 
upon looking for the means of applying concentration relations as 
if Lewis had made use of a clever dodge. In reality he has simply 
expressed in a form which he has developed into a self-consistent 
system that which is the more directly determined experimentally. 
This is at once evident in the definition of activity by the fol- 
lowing postulates. 

1. When the activity of a substance is the same in two phases, that 
substance will not of itself pass from one phase to the other. 2. When 
the activity of a substance is greater in one phase than in another, the sub- 
stance will pass from the one phase into the other, when they are brought 
together. 

With these postulates Lewis proceeds to develop a self-consist- 
ent system in which it appears that in a "concentration cell" the 
ratio of activities is related to the E. M. F. by the equation 

_ ,, _ RT , activity 1 

E. M. F. = — In ^— 

nF activity 2 

Only at infinite, or very high dilution, when a solution approaches 
an "ideal" solution, does the more familiar relation of concentra- 
tion hold true. So long as the limitations were well understood it 
was permissible to speak of the hydrogen electrode method -as a 
means of determining relative concentrations. If one is willing to 
use Lewis' terms he would be more precise to speak of the hydro- 



STANDARDIZATION OF pH MEASUREMENTS 279 

gen electrode method as a means of determining relative hydrogen 
ion activities. 

We may note at this point that if we adopt the activity con- 
cept and if we refer electrode potential differences to that of the 
normal hydrogen electrode, confusion is introduced by the use 
of the term normal concentration in the definition of the normal 
hydrogen electrode. This is clarified if we adopt the definition 
of Lewis and .Randall: "A solution is said to be at (hypothet- 
ical) molar concentration with respect to hydrogen ion when the 
activity of hydrogen ion in this solution is n times as great as in 
1/n M solution of hydrogen ion, where n is a large number." | 

The use of the equation given above instead of the equation 
involving concentrations only shifts our immediate ' problem to 
a new position. We are still concerned with a ratio and must 
somehow establish a point of reference. At first sight we have 
also shifted to a position from which it is difficult to obtain any 
connection with weights of materials (concentrations). 

A formal relation between activity and concentration may be set up 
by the use of the socalled activity coefficient. Of this Lewis and Randall 
(1921) state: ' The term activity coefficient has been used in two senses, 
sometimes to mean the ion activity divided by the assumed ion molality, 
and sometimes to express the ion activity divided by the gross molality 
of the electrolyte." 

Now, if we have a solution of HC1 so dilute that we may assume 
the activity of the hydrogen ion equal to the concentration, 
and if at the same time the solution is so dilute that we may assume 
complete ionization, we have a starting point, for then the hydro- 
gen ion activity may be determined from the analytical concen- 
tration of the HC1. By the use of the electromotive force equation 
relating activities we can establish by experiment the relative 
activity of the hydrogen ion in a more concentrated solution. 
But there is little assurance that such measurements of relative 
ictivity have been made with the highest accuracy because of 
he experimental and theoretical difficulties of liquid junction 
Dotential differences. 

By means of conductivity some idea is obtained of ion concentrations 
nd by means of activity coefficients activity and concentration are 



280 THE DETERMINATION OF HYDROGEN IONS 

related. But since exact treatment of the subject necessitates discussion 
of assumptions the reader is referred to the original literature. 

Using the most probable values for the corrected degree of 
dissociation of hydrochloric acid solutions, the E. M. F. of the 
cell: normal calomel electrode-hydrogen electrode in N/10 or 
N/100 HC1, and the estimated contact potential difference at the 
liquid juncture, Lewis and Randall obtained the value 0.2776 for 
the difference of potential between the normal calomel and the 
normal hydrogen electrodes at 25°. This value was revised to 
0.2828 by Lewis, Brighton and Sebastian (1917). Direct compari- 
son with N/10 KC1 calomel electrode, as will be noted later, gave 
0.3357 as the potential value of this electrode including a slight 
liquid junction potential difference. 

Now let us consider the values hitherto used in biochemical 
work. 

In S0rensen's work, published prior to the adoption of the pres- 
ent standard value of the Weston standard cell, the basis for the 
particular cell whose value he gave was not stated. If it was the 
1.01863 used in Germany prior to 1911 the correction of S0ren- 
sen's data to the present international volt will not be significant. 
Doubtless the international standard was used in Denmark when 
S0rensen (1912) published the summary of the data of S0rensen 
and Koefoed. Their values involve two assumptions; first that 
liquid junction potential differences were eliminated by the Bjer- 
rum extrapolation; second, that in the calculation of the theoreti- 
cal difference of potential between the normal hydrogen electrode 
and the hydrogen electrode in the hydrochloric acid solutions 
used, the correct hydrogen ion concentration was given by con- 
ductance data. As already stated there is serious doubt of the 
validity of the last assumption. Even so we ought, by using the 
same degree of dissociation for hydrochloric acid solutions, to 
reconcile S0rensen's value with that of Lewis, Brighton and Se- 
bastian. S0rensen assumed 91.7 per cent dissociation of 0.1m 
HC1 at 18°C. Employing the same value at 25°, as an approxima- 
tion, we would find that the hydrogen electrode in 0.1m HC1 
should be 0.0614 volts more negative than a "normal" hydrogen 
electrode. If however we take "the corrected concentration of 
H+ in 0.1m HC1 as 0.0816" (Lewis, Brighton and Sebastian) then 
the difference would be 0.0643. The correction 0.0029 should 



STANDARDIZATION OF pH MEASUREMENTS 281 

bring S0rensen's value into harmony with that of Lewis, Brighton 
and Sebastian. However, they are: 

Lewis, Brighton and Sebastian 0.3357 

S0rensen (corr.) . 3347 

The discrepancy of 0.0010 volt remains to be explained. That it 
may be ascribed partly to an involved potential difference be- 
tween N/10 KC1 and N/1 KC1 which has not been noted in the 
discussion and partly to an excess correction for diffusion poten- 
tial through the use of the Bjerrum extrapolation seems prob- 
able from the treatment accorded this subject by Fales and 
Vosburgh; but if we attempt to correct S0rensen's data by the 
use of the curves given by Fales and Vosburgh the discrepancy 
noted above widens. It is of no particular importance to attempt 
further to reconcile the two values because S0rensen's original 
data (1909) show wide variations in the E. M. F.s. of the chains 
in which hydrochloric acid was used. One might therefore jump 
to the conclusion that S0rensen's value is unworthy of further 
consideration now that we have a more probable value. It must 
be emphasized however that we are not so much concerned with the 
reliability of S0rensen's original data as we are with the fact that 
the value thereby assigned to the tenth normal calomel electrode 
has been widely used in the study of hydrogen electrodes in solu- 
tions which exhibit comparatively low diffusion potentials against 
KC1 and which furnish hydrogen electrode potentials reproducible 
with a considerable degree of precision. Because of this, because 
of the fact that the S0rensen value and other comparable values 
have standardized an enormous amount of biochemical data we 
regard it as important to consider the old value further. 

When S0rensen's value has not been used directly it has been 
used indirectly in the taking over of pH values assigned to standard 
solutions such as standard acetate. In Walpole's study of acetate 
mixtures he appears to have been consistent in using the value 
assigned by S0rensen to the tenth normal calomel electrode referred 
to the normal hydrogen electrode under one atmosphere of hydro- 
gen plus vapor pressure. He obtained a value for the hydrogen 
electrode potential in standard acetate agreeing with that found by 
S0rensen and by Michaelis. In Clark and Lubs' study of phthal- 
ate, phosphate and borate buffer mixtures they applied the Bjer- 



282 THE DETERMINATION OF HYDROGEN IONS 

rum extrapolation, and, with the qualifications stated in their 
paper reached a value 1 for their tenth normal calomel electrode 
in substantial agreement with S0rensen's. 

Palitzsch doubtless used the S0rensen value, which he originally 
aided in determining, in his study of borate buffer mixtures. 

A variety of similar channels might be followed to, show that 
in the biochemical literature there is substantial agreement so far 
as the assumed difference between the tenth normal calomel and 
the normal hydrogen electrodes is concerned. Since the liquid 
junction potential differences between saturated KC1 and the 
buffer solutions and physiological fluids dealt with in biochemis- 
try are of a low order of magnitude it seems fair to assume that 
the more precise biochemical data are fairly well standardized, 
though not necessarily accurate. The agreement was further- 
more encouraged in other lines of investigation by the 
recommendation of Auerbach (1912) when, in his summary of 
the work of the "Potential Commission," he recommended the 
use of the tenth normal calomel as a working standard because 
of its low temperature coefficient, and assigned the value 0.337 
for use between 20° and 30°. 

On the one hand, then, we have what may be regarded as a 
tacitly accepted and not yet precisely formulated standardization 
of the tenth normal calomel electrode; and on the other hand a 
distinctly different value for the tenth normal calomel electrode 
that is doubtless more nearly correct, though the details by which 
the value was reached are not presented. The biochemist is thus 
placed in an' embarrassing position. Before making a choice he 
may consider the present situation in our knowledge of the tem- 
perature coefficients of calomel electrodes. 

In dealing with the temperature coefficients it will be distinctly 
understood that we are not concerned with the temperature co- 
efficient of the absolute difference of potential between mercury 
and solution but rather with the temperature coefficient of the 
calomel electrode in the cell: calomel electrode-normal hydrogen 

1 Clark and Lubs give their E. M. F.'s reduced to refer to the normal 
hydrogen electrode under a standard hydrogen concentration rather than 
the standard pressure usually used. Since the calomel values were also 
referred to the same basis the pH values given by these authors remain as 
if the customary procedure had been followed. 



STANDAHDIZATION OF pH MEASUREMENTS 



283 



electrode, when the potential difference at the normal hydrogen 
electrode is defined to be zero at all temperatures. Unfortunately 
we have little data upon this temperature coefficient which are 
both accurate and extensive. Therefore one who chooses to take 
over the better value for the tenth normal or the normal calomel 
electrode will still be left in the predicament of not knowing the 
precise value to use at temperatures other than 25°C. 

We can only reach approximate values in the following manner 
and compare the results with comparatively old experimental data. 

Lewis and Randall (1914) have derived a provisional tempera- 
ture coefficient for the normal calomel electrode which indicates 
that the values are not a linear function of the temperature. The 
derivation of these authors as applied to the tenth normal elec- 
trode will be followed, but some new values obtained since the 
writing of their paper will be introduced. 

For the cell 



PtH, 



HC1 
0.1 M 



Hg 2 Cl 2 Hg 



Lewis and Randall give the empirical equation 

E = 0.0964 + 0.001881T - 0.000,00290^ 

whence 

dE/dT = 0.001881 - 0.00000580T 

For present purposes this conforms closely enough with Ellis' 
(1916) data. 
It is now assumed that the temperature coefficient of the cell 



will apply to 



PtH, 



PtH 2 


HC1 
0.1 M 


Hg 5 


I* 


H( 
0.1 


31 
M 


K 
0.1 


CI 
M 



Hg 2 Cl 2 Hg 



if the tenth molar hydrochloric acid calomel cell has the same 
potential as the tenth molar KC1 calomel cell. Compare however 
Lewis, Brighton and Sebastian (1917) who give 0.0012, and Mac- 
Innes (1919) who gives 0.0. 



284 THE DETERMINATION OF HYDROGEN IONS 

For the cell 



PtH 2 



HC1 
0.1 M 



H+|PtH 2 
M 



For the cell 






Hg Hg 2 Cl 2 


KC1 


KC1 




0.1 M 


1.0 M 



Lewis, Brighton and Sebastian give 0.0644. Assuming that in 
this cell the E. M. F. is proportional to the absolute temperature, 

dE 

3^, = 0.00022. Hence for the tenth molar KC1 calomel electrode 
ul 

against the normal hydrogen electrode 

-45 = 0.00166 - 0.00000580T. 
dT 



Hg 2 Cl 2 Hg 



the author finds at 20° 0.0519, and at 30° 0.0536. Interpolation 
between these values on the assumption that the E. M. F. is a 
linear function of the temperature gives an E. M. F. at 25° which 
is within 0.15 millivolts of that found by Lewis, Brighton and Se- 
bastian, and a linear temperature coefficient of 0.000,17. Sauer's 
value at 18° is 0.0514 and that of Fales and Vosburgh at 25° is 
0.0524. Neither of these values falls in with those mentioned 
above but when taken by themselves and with the 15° value, 
0.0509, given in the footnote of the paper by Fales and Vos- 
burgh (1918) they furnish a temperature coefficient of the same 
order. 

With these data we can start from the value 0.2828 as that of 
the normal calomel electrode (Lewis, Brighton and Sebastian, 
1917) at 25°; or with S0rensen's (1912) value, 0.3380, for the tenth 
normal calomel electrode at 18° and treating each set separately 
we reach the comparisons shown in table 49. 

Bjerrum's values at 0°, 25° and 75° do not fit in with the calcu- 
lations given above. 

The values given above are admittedly uncertain and are to be 
regarded as provisional in lieu of the experimental data that is 
needed. It may be emphasized however that there is good reason 
to believe that the temperature coefficient for the tenth normal 
electrode is much lower than that of the normal calomel electrode. 



STANDARDIZATION OF pH MEASUREMENTS 



285 



Since we can as yet only make a good guess of the temperature 
relations it seems wise to choose as a standard the calomel elec- 
trode with the smaller temperature coefficient and thus lower one 
chance of error. This fortunately has been, for the most part, 
the practice in biochemical work although it runs counter to pref- 
erences which will not be discussed. 

TABLE 49 





LEWIS 




TENTH 
AGAINST 
NORMAL 
CALOMEL 




S0RENSEN 




t 


1.0 N 


0.1 N 


1.0 N 


0.1 N 


0.1 N 
Found 


18 


0.2844 


^-0.3360 

T 


0.0516 


0.2864 


<-0.3380 

1 


0.3380 


20 


0.2840 


<-0.3359 

T 


0.0519. 


0.2860 


<-0.3379 

1 


0.3378 


25 


0.2828 


— >0.3356 

I 


0.0528 


0.2S48 


<— 0.3376 
I 




30 


0.2817 


«-0.3353 


0.0536 


0.2836 


<-0.3372 

I 


0.3370 


37.5 










. 3364 

I 




40 










3360 

1 


0.3359 


50 










3341 

1 


0.3344 


60 










0.3317 


0.3321 



Approximate temperature coefficient of normal calomel electrode 
-0.000,23. 

Approximate temperature coefficient of tenth normal calomel electrode 
-0.000,06. 

Let us then assume that this half cell, the tenth normal calomel 
electrode, is to be the standard to which all working electrodes 
are to be referred and let us consider finally the choice of values to 
be assigned. 

At 25°C. the difference between the values for the tenth nor- 
mal calomel electrode given in table 49 is 2 millivolts. A change 
of this amount would shift the values in the pH scale 0.03 unit pH. 
This is quite insignificant or within the experimental error in many 
biochemical studies. For certain purposes it is not insignificant. 
When carried into mass action relations it might be serious but 
in such relations there are generally involved data taken over from 
conductance measurements. In such a situation therefore there 



286 THE DETERMINATION OF HYDROGEN IONS 

are involved complexities which are by no means covered by the 
mere selection of a more probable value for the standard electrode. 

We have already mentioned the fact that even if the value of 
Lewis, Brighton and Sebastian be absolutely correct at 25° we 
cannot assign accurately known values at temperatures other 
than 25°, and we have noted the more or less tacit assumption of 
standard values for various temperatures in the course of the 
development of biochemical applications. 

In addition to the difficulties mentioned above there is a funda- 
mental question which runs throughout all present-day calcu- . 
lations. As we have reiterated, all hydrogen electrode measure- 
ments are referred by one route or another to some experimental 
standard and the hydrogen ipn concentration or hydrogen ion 
activity, as the case may be, is estimated for this experimental 
standard by the use of theory which at present is in a state of 
flux. One's inclination is to accept the latest value advocated 
by the most advanced thought and yet it is an open question 
whether the inherent relativity of the whole subject will not force 
us ultimately to adopt an arbitrary standard. While certain 
.investigators are accepting the value for the normal calomel elec- 
trode given by Lewis, Brighton, and Sebastian, Bjerrum is apply- 
ing the theory of complete dissociation of salts and reaching a 
very different value. In the author's opinion it will be wise 
during the present transition period to adopt a provisional 
standard and in lieu of agreement reached in convention to let 
that standard be in harmony with that tacitly implied in the 
greater body of data. The author therefore suggests that the 
values in column 6 of table 49 be used as provisional stand- 
ards wherever there is no definite reason to require any other 
value. 

We can thus preserve uniformity in pH data and not introduce 
ill-considered changes which may need subsequent frequent re- 
vision before the present theoretical difficulties are removed or 
before the action of an international committee fixes a standard 
value. 

It may be objected that under such a procedure of standardiza- 
tion the symbol pH loses the precise significance which has been 

attached to it. It has always been defined as log — -:. If the 



STANDARDIZATION OF pH MEASUREMENTS 



287 



"concentration chain" does not determine with precision the ratio 
of two hydrogen ion concentrations but rather the ratio of two hy- 
drogen ion activities, and if, in addition, we adopt a standard of 
reference in the current use of the hydrogen electrode which is not 
strictly true, then pH is no longer expressive of the true value of 

log . We need not be concerned with the casuistry of this sit- 

uation. We need only remember that the more precise uses to 
which hydrogen electrode measurements may be put involve the- 
oretical difficulties which we are not yet prepared in every case 
to deal with accurately, 2 that in the more common uses the un- 
certainty is not of a serious magnitude and that it is preferable 
to maintain uniformity in the manner of stating experimental 
values. If we take care to put a definite and unequivocal meaning 
to experimental data, relieving them as far as possible from ill- 
defined presumptions, we maj r be pardoned for continuing to use 
in descriptive text and in approximate calculations "hydrogen 
ion concentrations." When we come to exact statements they 
will be found embodied in pH values of uniform experimental 
derivation. 

In summary then it is suggested that : 

1 . The following values shall be taken as the standard differences 
of potential, liquid junction potential differences being eliminated, 
between a tenth normal KCl calomel electrode and a hypothetical 
hydrogen electrode immersed in a solution normal with respect to 
the hydrogen ions, under one atmosphere partial pressure of 
hydrogen, and considered to have zero difference of potential 
between electrode and solution at all temperatures. 





TEMPERATURE 




18° 


20° 


25° 


30° 


37.5° 


40° 


Potential difference. . 


0.3380 


0.3379 


0.3376 


0.3373 


0.3364 


3360 



2. The standard experimental meaning of pH shall be the cor- 
rected difference of potential between the hypothetical normal 

2 In very many instances constants determined by conductivity methods 
are employed with precise electrode measurements without any critical 
examination whatever of their applicability. 



288 THE DETERMINATION OF HYDROGEN IONS 

hydrogen electrode and the hydrogen electrode under measure- 
ment (when this difference is derived by the use of the above 
values), divided by the numerical quantity 0.000,198,37 T. 

3. In every case it shall be specified whether the Bjerrum ex- 
trapolation with the use of 1.75n and 3.5n KC1 was used to elimi- 
nate liquid junction potentials or whether saturated KC1 was used 
and considered to eliminate liquid junction potentials. 

There are those who will prefer to use the saturated KC1 calomel 
electrode as a working standard. Its use eliminates the protec- 
tive devices required to guard the tenth normal calomel electrode 
against the saturated KC1 used as a liquid bridge. Michaelis 
(1914) has also noted that its temperature coefficient is such that 
it tends to balance the effect of fluctuations in the temperature of 
a calomel electrode-hydrogen electrode chain. Though there are 
involved in Michaelis' reasoning some factors which are yet un- 
certain this advantage may be granted. A practical system which 
embodies the merits of the saturated calomel electrode and which 
meets the requirements of the standardization suggested above is 
illustrated on page 183. In this system the saturated calomel elec- 
trode is the working standard whose value is given by careful com- 
parison at known temperatures with a set of tenth normal calomel 
electrodes. 

If any ultimate experimental standard other than the tenth 
normal calomel electrode be used it is suggested that for the 
present it be brought into harmony with the above system, which 
is the system that has practically governed past measurements, 
and that fundamental revision of any standard await concerted 
action based upon thorough investigation of both experimental and 
theoretical data. 

These suggestions simply put into definite form the current 
procedure with the recognition on the one hand that the precise 
use of electrode data involve many theoretical difficulties and on 
the other hand that the use of such data for the approximate cal- 
culation of hydrogen ion concentrations had best be standardized 
for the sake of uniformity in the records to be handed on to the 
future. 



CHAPTER XX 
Supplementary Methods 

When any process has been found to be controlled by the con- 
centration of the hydrogen or hydroxyl ions, when the quantitative 
relations have been established and contributory factors are con- 
trollable, there is established a possible means of estimating the 
concentration of the hydroxyl or hydrogen ions. Many such in- 
stances are known. From among them a few may be chosen for 
their convenience. They are spoken of here as supplementary 
methods because they are superseded in general practice by indi- 
cators and the hydrogen electrode. Several have historical value 
because they were used in establishing the laws of electrolytic 
dissociation. Others have value because they are available 
either for checking the customary procedures or for determina- 
tions in cases where there is reason to doubt the reliability of indi- 
cator or hydrogen electrode measurements. 

An instance of the procedure outlined above is the following. 
Clibbens and Francis (1912) found that the decomposition of 
nitrosotriacetonamine into nitrogen and phorone is a function of 
the catalytic activity of hydroxyl ions. Francis and Geake (1913) 
then applied the relation to the determination of hydroxyl ion 
concentrations, Francis, Geake and Roche (1915) improved the 
technique, and then McBain and Bolam (1918) used the method 
to check their electrometric measurements of the hydrolysis of 
soap solutions. 

It is just in such checking that the value of these so-called sup- 
plementary methods will be appreciated. But, since they will find 
only occasional use and under circumstances which will require a 
detailed consideration of their particular applicability, there 
seems to be no reason to do more than indicate a few of the methods 
in brief outline. 

THE QUINHYDRONE ELECTRODE 

We have already seen in Chapter XVI that, when pH is less 
than about 7, a platinum electrode in the presence of hydroqui- 

289 



290 THE DETERMINATION OF HYDROGEN IONS 

none and quinone should show a potential difference, which, 
when referred to the normal hydrogen electrode as a standard 
may be expressed by the equation 

RT , RT [Sdl 

E h = E k + ~y In [H+] - ^ In jg-j (66) 

where Eh is the observed single electrode potential difference, 
Etis a constant and [Sd] and [S q ] are the total concentrations of 
hydroquinone and quinone respectively. We have also previously 
noted that, under the limitations specified, Eh becomes a linear 

rs i 

function of pH when the ratio — ; is kept constant and the tem- 

[bqj 

RT 

perature is constant. (At 30°C, for instance, — In [H+] is 

- 0.06 pH.). 

Now quinone and hydroquinone combine in equimolecular 
proportions to form quinhydrone. (To distinguish this product 
from similar compounds such as that formed from toluenequinone 
and toluenehydroquinone it may be called benzoquinhydrone.) 
In aqueous solutions the reaction is reversible, 

quinone + hydroquinone ^ quinhydrone 

and since the solubilities are low, the addition of solid quinhy- 
drone is a convenient way of providing a solution with a mixture 
of quinone and hydroquinone. We must be careful, however, not 
to assume that the two are necessarily present in equimolecular 
concentrations. We may assume that the solid quinhydrone 
maintains a constant concentration of undissociated quinhydrone 
in solution. This dissociates and we have the equilibrium condi- 
tion where D represents hydroquinone, Q quinone and QD quin- 
hydrone: 

[Q][D] 



[QD] 



= Ki, and since [QD] is constant, 



[Q][D] = K B , where K 8 is the so-called solubility product. 
From this it is evident that only the product [QJ[D] is kept con- 
stant. Ionization of D (hydroquinone) is certainly of funda- 
mental importance as outlined in Chapter XVI and we therefore 
cannot neglect to consider its effect in the above equation. But 



SUPPLEMENTARY METHODS 291 

we have already brought the electrode potential equation into 
such a form and simplified it with the assumption that it is to 
be used in the region of inappreciable dissociation of D so that 
we are able at once to say that the very slight ionization of the 

rs i 

hydroquinone (D) will not appreciably alter the ratio — — : from 

IpqJ. 

unity. Thus in acid solutions the presence of solid quinhydrone 
maintains a practically constant, unit ratio of its dissociation 
products. The last term in equation (66) becomes zero, and 
we have 

E h = E k - 0.000.198 T pH (67) 

When Ek has been established a measurement of Eh enables 
one to calculate pH. 

Biilmann (1920) and Biilmann and Lund (1921) have devel- 
oped the "quinhydrone electrode" for practical use and employ 
the above equation, derived, however, in another way (assuming 
the electrode to function as an actual hydrogen electrode. See 
Chapter XVI). 

For the preparation of quinhydrone Biilmann (1921) employed 
the method of Valeur. Later Biilman and Lund (1921) found 
it practicable to prepare the quinhydrone as follows: 

One hundred grams of ferric ammonium alum in 300 cc. water 
at 65°C. is turned into a warm solution of hydroquinone in 300 
cc. water. The quinhydrone precipitates as fine needles. Cool 
the mixture in ice and then filter with suction washing the needles 
three or four times with cold distilled water. Yield, 15 to 16 
grams. It is stated that the trace of iron remaining after this 
process is without serious effect. 

To form a "quinhydrone electrode" Biilmann employs a vessel 
similar to those used for calomel electrodes but with a fairly 
large platinum electrode (blank platinum). A little quinhydrone 
is mixed with the acid solution under examination, placed in 
the vessel with the platinum electrode and connected with a 
saturated or other calomel electrode. 

Biilmann determined E k in equation (67) by simply fixing the 
pH at a known value with definite buffer solutions and measuring 
:he difference of potential between a quinhydrone electrode in 






292 THE DETERMINATION OF HYDROGEN IONS 

this solution and a hydrogen electrode in the same buffer without 
quinhydrone. He gives: 



Temperature 


Ek 


18 


0.704 


25 


0.699 



Besides the benzoquinhydrone electrode Biilmann also describes 
electrodes formed with the xylene and toluene homologues. 

Biilmann and Lund describe capillary vessels for use with 
such electrodes. 

S0rensen, S0rensen and Linderstr0m-Lang (1921) discovered 
that there is a "salt error" with the quinhydrone electrode which 
becomes very appreciable at salt concentrations of the order of 
M/5. This they ascribe to an altering ratio of activities for the 
quinone and hydroquinone with change in salt content. 

By methods for the detail of which the reader is referred to 
the original papers it is predicted that the ratio of the activities 
of hydroquinone and quinone is defined when the solution is 
saturated with quinhydrone and one of the components, hydro- 
quinone or quinone; and that under these circumstances there 
should be less "salt error." There may then be formed what 
Biilmann and Lund call the hydro-quinhydrone electrode and the 
quino-quinhydrone electrode. 

The hydro-quinhydrone electrode is similar to the quinhydrone 
electrode described above except that there is present besides 
solid quinhydrone, solid hydroquinone. At 18°C. the Ek value 
of this electrode is given by Biilmann and Lund as 0.618. 

In the quino-quinhydrone electrode there is present besides 
solid quinhydrone, solid quinone. At 18°C. the Ek value of this 
electrode is 0.756. In each case the platinum of these electrodes 
is positive to the platinum of the hydrogen electrode by the given 
values. 

There are a number of details in the use of these electrodes 
which require further study and the reader is referred to the orig- 
inal literature for those which hrve already received attention. 

Aside from the great interest of the subject as an example of 
the general relations pointed out in Chapter XVI the electrodes 
developed by the Danish investigators should be useful in those 
cases where the hydrogen of the hydrogen electrode is seriously 
attacked by the components of a solution. But by the same token 



SUPPLEMENTARY METHODS 293 

the quinhydrone electrode cannot be used when the reduction 
potential of a solution is such as to seriously alter the ratio of the 
hydroquinone and quinone. In either case, however, there re- 
mains the possibility of taking advantage of the slowness with 
which some oxidation-reduction reactions come to equilibrium 
and experience alone will indicate the limitations of usefulness. 
Independently of the Danish investigations Granger and Nel- 
son (1921) worked out some of the relations involved in the quin- 
hydrone electrode. 

CONDUCTIVITY 

The conductivity of a solution is dependent upon the concen- 
trations of all the ions and upon the mobilities of each. It is 
therefore obvious that a somewhat detailed knowledge of the con- 
stituents of a solution and of the properties of the constituents is 
necessary before conductivity measurements can reveal any ac- 
curate information of the hydrogen or hydroxyl ion concentra- 
tion. Even when the constituents are known it is a matter of 
considerable difficulty to resolve the part played by the hydrogen 
ions if the solution is complex. However, the mobilities of the 
hydrogen and hydroxyl ions are so much greater than those of 
other ions (see page 163) that methods of approximation may be 
based thereon. If, for instance, a solution can be neutralized 
without too great a change in its composition it may happen that 
with the disappearance of the greater part of the hydrogen ions 
there will appear a great lowering in conductance. Then, with 
the appearance of greater hydroxyl ion concentration, the conduct- 
ance will rise. The minimum or a kink in the curve is 
a rough indication of neutrality. Thus the conductivity method 
is sometimes useful in titrations. See Kolthoff for details and 
references. 

The elementary principles of conductivity measurements will 
be found in any standard text of physical chemistry but the more 
refined theoretical and instrumental aspects are only to be found 
by following the more recent journal literature. 



294 



THE DETERMINATION OF HYDROGEN IONS 



CATALYTIC DECOMPOSITION OF NITROSOTRIACETONAMINE 

The reaction taking place is represented in outline by the 
following equation : 

p n /^ 2 * C(CH 3 ) 2 \ M . ma _^ nrk /CH: C(CH 3 ) 2 , v , w n 
C0 \CH 2 • C(CH 3 ) 2 / N N ° "* C0 \CH: C(CH 3 ) 2 + Na + Hz ° 

The original quantity of nitrosotriacetonamine is known and the 
extent of the decomposition at the end of measured intervals of 
time is measured by the volume of nitrogen evolved. 




Fig. 41. Vessel for the Catalytic Decomposition op 
Nitrosotriacetonamine 

Francis, Geake and Roche (1915) use the vessel shown in figure 
41. The tap of the reaction vessel contains a cup B of 7 to 10 
cc. capacity into which the alkali or the nitrosoamine can be intro- 
duced through F. The solution is then shut in by turning the key 
through a right angle. The cup becomes a part of the reaction 
chamber A on turning the key as shown in the figure. The ves- 
sel is immersed in a thermostat and shaken during the whole ex- 
periment. The holes at E and E' permit the cup B to be bathed 



SUPPLEMENTARY METHODS 295 

by the thermostat liquid and so reach thermal equilibrium at the 
same time as the chamber A. The tube R connects with a con- 
stant volume burette where the evolved nitrogen is collected and 
its pressure read. The tube D is used for washing out the vessel 
and for filling it with nitrogen when the reaction has to be con- 
ducted in an atmosphere free from oxygen. 

The unimolecular equation, using the pressure method is 

k = 2 ' 303 lo Pc ° ~ P ° 
t ° g P. - P t 

where P is the pressure at the time taken as zero, P t the pressure 
taken at the time t and Poo the so-called infinity reading at the 
end of the experiment. The unit of time taken is the second. At 

30°, — ^— = 1.92. 
[OH-] 

It was found that the constants obtained with nitrosotriace- 
tonamine commence to drift when the ion concentration reaches 
O.Oon while at 0.35n the drift ceases and the method is again 
applicable. To bridge the gap it was found that nitroso-vinyl- 
and isobutyl-diacetonamines could be used. 

For temperature coefficients and for the influence of neutral 
salts etc. the original paper may be consulted. 

CATALYTIC DECOMPOSITION OF DIAZOACETIC ESTER 

Bredig and Fraenkel (1905) have described the following reac- 
tion as applicable to the determination of hydrogen ion concen- 
trations. 

N 2 CH.C0 2 C 2 H 5 + H 2 = N 2 + (OH)CH 2 C.C0 2 C 2 H 5 
The nitrogen evolved from time to time is measured and the 
values used in the equation 

1 ° 

k = „ dn . n , log 



0.4343 t a - x 

vhere a is the total gas at the end of the reaction, x the gas after 

k 
lme t minutes and k the reaction constant. At 25°C, ^r, = 32.5. 

The method was applied with only partial success by Hober 
1900) to blood. Van Dam (1908) used it in the examination of 
ennet coagulation of milk. 






296 THE DETERMINATION OF HYDROGEN IONS 

THE INVERSION OF CANE SUGAR 

This has been a favorite subject of study by those interested 
in the catalytic activity of the hydrogen ion. It has been 
used in a number of instances for the determination of the 
hydrogen ion concentration of biochemical solutions, but, like 
all catalytic processes, its close study has revealed a number of 
complicating factors which necessitate the greatest caution in the 
interpretation of results. 

So numerous are the papers dealing with sugar hydrolysis by 
acid that the reader is referred to the very thorough review by 
Woker for the older work. For the more recent investigations 
see, for example, Jones and Lewis, 1920. 

CATALYSES IN GENERAL 

Pending further development of the theory of strong electrolytes 
and of the "salt effect", the investigator, using one or another 
of the above catalysis methods merely as a check, can place his 
data upon a reproducible basis by using the following system of 
comparison. Determine the pH values of a series of buffer 
solutions lying within the pH range expected of the unknown, 
and having total salt concentrations comparable to that of the 
solution to be tested. Under parallel conditions determine the 
catalytic activity of knowns and unknown. Assume that the 
result with the buffer agreeing closest to that of the unknown 
indicates that this buffer and the unknown are at the same pH 
and check by various modifications of buffer. 

MISCELLANEOUS METHODS 

Were it worth while there could be compiled under this heading 
a wide variety of phenomena which have actually been used to 
determine approximately the hydrogen ion concentration of a 
solution. We may instance the precipitation Of casein from milk 
by the acid fermentation of bacteria. This has not been clearly 
distinguished in all cases from coagulation produced by rennet- 
like enzymes; but, when it has been, the precipitation or non-pre- 
cipitation of casein from milk cultures has served a useful purpose 
in the rough classification of different degrees of acid fermentation. 



SUPPLEMENTARY METHODS 297 

In like manner the precipitation of uric acid or of xanthine has 
been used (Wood, 1903). 

The alteration of the surface tension of solutions (Windish and 
Dietrich, 1919-1921), the distillation of ammonia (Vely 1905), dis- 
tribution ratios between different solvents, and various other 
methods have been used to furnish data for the estimation of 
hydrogen or hydroxyl ion concentrations. 



CHAPTER XXI 

Applications 

Finally, acidity and alkalinity surpass all other conditions, even 
temperature and concentration of reacting substances, in the influence 
which they exert upon many chemical processes. — L. J. Henderson. 

It is because of the great variety of applications in research, 
routine and industry that the theories and devices outlined in the 
previous chapters have been developed. The physical chemist 
sees in them the instruments of approximation or of precision 
with which there have been discovered orderly relations of ines- 
timable service to the analyst and with which there have been 
established quantitative values for affinity or free energy. The bio- 
chemist might almost claim some of these methods as his own, not 
only because necessity has driven him to take a leading part in 
their development, but also because their application has become 
part of his daily routine in very many instances. 

As mentioned in the preface to the first edition the applications 
have become so numerous and in many cases so detailed that the 
time has come for a redispersion among the several sciences of 
the material that has from time to time been grouped about the 
activity of the hydrogen ion. This chapter therefore is written 
only as a cursory review with the hope that it may be of service 
to the student by revealing the interdependence of specialized 
lines of research, by suggesting how mistakes still current have 
been eliminated by those who realize the importance of the sub- 
ject and by furnishing a rough index to our incomplete bibliog- 
raphy of a voluminous literature. 

In the compilation of the bibliography, of which this chapter 
constitutes an index, no attempt has been made to include all of 
the very numerous instances in which the activity of the hydrogen 
or the hydroxyl ions has been found to influence the course of spe- 
cific chemical reactions, such as the hydrolysis of polysaccharides, 
special oxidations and condensations, or the nature and accuracy 
of the numerous color tests used for the qualitative recognition of 
special chemical groupings. The reader will find in Woker's ex- 

298 



APPLICATIONS 299 

tensive monograph, Die Katalyse, not only a very complete re- 
view of the older, widely scattered literature upon these aspects 
of hydrogen and hydroxyl ion activity but also an abundance of 
material which still remains to be reworked with the more modern 
methods. 

In the classification of the bibliography no attempt has been 
made to place the references in strictly logical catagories, nor 
has it been practical to make a minute subdivision by subjects 
with numerous cross references. The grouping is by subjects 
which are of particular current or historical interest or which 
fall within the provinces of special branches of science. 

General Reviews. Excellent general reviews of biochemical 
applications are S0rensen's article in Ergebnisse der Physiologie, 
1912, and MichaekV monograph Die W asserstoffionenkonzentra- 
tion, 1914. As we go to press there comes to hand the first part 
of the 1922 revised edition of this excellent monograph. This 
first part covers in extended form the theoretical foundations 
briefly treated in the first edition and deals in more- or less detail 
with many subjects briefly touched upon in the following pages. 
Prideaux has compiled a great deal of valuable data in The Theory 
and Use of Indicators, London, 1917. In this English work will 
be found the more important matter which Bjerrum (1914) 
embodied in his monograph on the theory of titration and which 
Noyes had previously summarized in his paper "Quantitative 
application of the theory of indicators to volumetric analysis," 
(1910). The analyst will find a wealth of helpful suggestions in 
Stieglitz' Qualitative Analysis. A review of the indicator method 
which is of some general interest, although written specially for 
the bacteriologist, will be found in The Journal of Bacteriology, 
2, nos. 1, 2 and 3 (Clark and Lubs, 1917). 

Those who desire to review the theory of electrolytic dissociation 
with special reference to its bearing on electrode measurements 
will find useful LeBlanc's Text Book of Electrochemistry (1907). 

Among several papers which may be called classics in biochem- 
istry there will be recognized the preeminence of S0rensen's Etudes 
enzymatiques, II, from the Carlsberg Laboratory in Copenhagen 
and Das Gleichgewicht zwischen Basen und Sduren im tierischen 
Organismus by Henderson of Harvard. 

The Theory of Titration is so closely allied with the more 



300 THE DETERMINATION OF HYDROGEN IONS 

general applications of indicators and the hydrogen electrode that 
it may well be taken from the alphabetic arrangement to be fol- 
lowed and treated before taking up some general considerations. 

The stress which has come to be laid upon that factor of "acid- 
ity" with which we have been dealing should not detract from the 
true importance of the estimation of total acidity or alkalinity by 
titration. 

But the theory of titration is only a special form of the theory 
with which we have been concerned up to this point; so that we 
are prepared to sketch in outline those salient features of the well- 
ordered theory which has displaced the loose empiricism of other 
days. 

In figure 42 are shown the titration curves of hydrochloric, 
acetic and boric acids, determined as outlined in Chapter II. The 
ordinates of figure 42 are pH values and the abscissas cubic centi- 
meters of N/10 NaOH added to 10 cc. N/10 acid. At the side 
of the main part of the figure are representations of the color trans- 
formations of two indicators (see Chapter IV). 

Although the indicator curves are drawn at one side of the figure 
the reader will readily see from the theory described in Chapter 
IV that they could have been placed in the main figure parallel 
to the titration curves if the abscissas had been made percentage 
neutralization. 

A more complete picture of the conditions of titration would 
be shown had the curves been extended to indicate what happens 
when the "end-points" are overstepped. The reader may pic- 
ture this for himself by imagining that the curve for boric acid 
continues with the slope shown at 11 and then flattens out be- 
tween 12 and 13, and that the other curves, after passing pH 10, 
sweep to the right to join the extended boric curve. 

When all but a very small part of the hydrochloric acid has been 
neutralized there comes a sharp break in the titration curve. On 
the addition of the last trace of alkali required for complete neu- 
tralization the pH of the solution plunges to the alkaline region. 
In this precipitous change the pH passes the range of methyl red, 
and, with an amount of alkali that will be detected only by careful 
observation, it passes into that range of pH where phenolphthalein 
shows its various degrees of color. Therefore, with the exclusion 
of carbon dioxid, either indicator may be used to indicate the "end 



APPLICATIONS 



301 



point" of this titration. The case is very different in the titration 
of acetic acid. Here we have an acid whose dissociation constant 
(see Chapter I) is so low that the flat portion of the titration curve 
lies in that region of pH where methyl red shows its various de- 



1 

2 
3 

A 




• 




^CV 






























5 
6 

7 

8 

9 

10 
pH 






^<^c 


4£rr> 


























































^^ 


4£*d 




















i 


I A 


1. t 


> I 


i 1 








Fig. 42. Titration Curves of 10 cc. N/10 Acids with N/10 NaOII 



302 THE DETERMINATION OF HYDROGEN IONS 

grees of color. In other words the apparent dissociation constant 
of methyl red is not far from that of acetic acid. Therefore, as 
the titration of acetic acid proceeds, and long before the neutraliza- 
tion of the acetic acid is complete, methyl red has been partially 
transformed and at last is so extensively transformed that no 
marked change of color is observed when the pH of the solution 
abruptly changes with complete neutralization of the acetic acid. 
It is at once evident why an indicator with the properties of 
phenolphthalein must be used in such a case. In the titration of 
a still weaker acid, such as boric acid, phenolphthalein becomes 
comparable to methyl red in the latter's conduct in acetate solu- 
tions. To titrate boric acid it must be combined with glycerine 
or mannitol to form a stronger acid. See Liempt (1920). 

The titration curve of boric acid is representative of the conduct 
of many of the weak acidic groups found in the substances of 
biochemical interest. 

Sometimes by a judicious selection of indicators it is possible to 
titrate in succession a mixture of two acids. For instance A. B. 
Clark and Lubs (1918) have called attention to the advantages of 
the two color transformations of thymol blue. The color trans- 
formation of thymol blue in the acid range is such that it may be 
used to indicate the approximate end point of hydrochloric acid 
in the presence of acetic acid ; and the second color change occurs 
in a region of pH such that it will indicate the end point in the 
titration of the acetic acid. A. B. Clark and Lubs (1918) and Lubs 
(1920) have examined other similar uses of this indicator. 

The principles thus briefly outlined apply to the titration of 
bases with strong acids, but, of course, with the direction of pH 
change reversed and with the end points tending to He on the acid 
side of pH 7.0. A hydrogen ion concentration of 10 _7 n or pH 7.0 
is called the neutral point because it is the concentration of both 
the hydrogen and the hydroxyl ions in pure water; but it is evi- 
dently seldom the practical or even the theoretical point of neu 
trality for titrations. 

As phenolphthalein is the more generally useful indicator for 
the titration of acids with strong bases so is methyl red the more 
generally useful indicator in the titration of bases with strong acids. 
Each fails, however, when the acid or base is very weak, and each 
may be replaced by a more suitable indicator in special cases. 



APPLICATIONS 303 

For the treatment of these cases the reader should consult the 
detailed description of the theory of titration in one of the papers 
mentioned above. 

Where high color or turbidity interferes with the use of indi- 
cators in titration the hydrogen electrode is often useful. See 
Bottger (1897), Hildebrand (1913) Michaelis (1917). Since it 
may be necessary only to detect the "break" in the titration curve, 
the hydrogen electrode system and potentiometer system used for 
this purpose may be very simple. The hydrogen electrode has 
the advantage that it may often be used where colorimetric tests 
are impracticable and that it may be linked electrically with auto- 
matic regulating and recording instruments such as Leeds and 
Northrup Company have devised for industrial use. 

Pinkhof (1919) has suggested special half-cells with single 
potentials equal to those of the end-points of titrations, thereby 
eliminating the necessity of a potentiometer. A galvanometer 
or electrometer indicates equalization of potentials and hence the 
attainment of the "end-point." 

In like manner one may use two hydrogen electrodes as de- 
scribed in Chapter IX. If one electrode is immersed in a solu- 
tion having the pH of the desired end-point, the attainment of 
this end-point in the other solution is indicated by the point of 
reversal of current in the galvanometer (Klopsteg, 1921). 

Since titrimetric determination of total acidity or basicity 
involves one or another method of estimating pH, the under- 
standing of the principles involved is essential to an intelligent 
interpretation of the values obtained in the titration of complex 
mixtures. In a great many instances there have been carried 
over to the titration of complex mixtures the rule-of-thumb method 
and the special interpretation first worked out by the analyst for 
the titration of strong acids and bases. Now it not infrequently 
occurs, especially among extracts of natural products, that there 
are present a variety of weak acids and bases; and no precipitous 
drop in the titration curve can be observed in the pH zones covered 
by the indicators very generally employed in such titrations. 
The situation is comparable with an attempt to titrate boric acid 
with phenolphthalein as indicator. No sharp "end-point" is 
observable. But there will always remain the distinctive value 
of a titration and wherever this cannot be precisely analyzed it 
should be stated in simple straightforward terms. 



304 THE DETERMINATION OF HYDROGEN IONS 

In the majority of cases the titration of such solutions reduces to a mere 
revelation of differences in total buffer action furnishing but one definite 
point on the titration curve. The procedure often followed is comparable 
with the practice of the ancient Romans who, according to Trillat (1916), 
(cf. Stephanides 1916) titrated natural waters with drops of red wine. 
While modern standards of concentration are more exact than the wine 
standard of the Romans their significance is largely lost by a choice of in- 
dicators as accidental as the Roman choice of the coloring matter of red 
wine. The frank admission that the content of acids in some complex 
solutions cannot be determined by titration need not destroy the value 
of the information gained by a titration if this information be correctly 
used. But too often the matter is carried to an extreme. In the routine 
methods for titrating milk a perfectly simple test has been so elaborated 
that it not only has become confusing to the chemist but so misleading to 
the creamery man that it is causing large economic losses. Often the 
initial pH of a solution is of greater significance than is the titration value 
obtained after juggling the solution with acid or alkali. Illustrations of 
this are to be found in the author's treatment of bacteriological culture 
media (Clark, 1915). 

Having followed some of the salient features of titration and 
found this procedure linked with the more general aspects of hy- 
drogen ion determinations the reader is reminded of those relations 
among acids and bases outlined in Chapter I which point to 
certain general considerations. 

General Considerations. As a comprehensive generaliza- 
tion it may be said that the hydrogen ion concentration of a solu- 
tion influences in some degree every substance with acidic or basic 
properties. When we have said this we have said that the hydro- 
gen ion concentration influences the great majority of compounds, 
especially those of biochemical interest. Such a generalization, 
however, would be misleading if not tempered by a proper appreci- 
ation of proportion. Rarely is it necessary to consider the ioniza- 
tion of the sugars since their dissociation constants are cf the order 
of 10~ 13 and their ionization may be generally neglected in the pH 
region usually encountered in physiological studies. Likewise 
there are zones of pH within which any given acidic or basic group 
will be found in dilute solution to be in a practically undissociated 
or fully dissociated state. Perhaps there is no more vivid way of 
illustrating this than by a contemplation of the conduct of indi- 
cators. Above a certain zone of hydrogen ion concentration 
phenolphthalein solutions are colorless. Below this zone (until 



APPLICATIONS 305 

intense alkalinity is reached) only the colored form exists. Within 
the zone the virage of a phenolphthalein solution is intimately 
related to the hydrogen ion concentration. The conduct of phen- 
olphthalein, which happens to be visible because of tautomeric 
changes which accompanj^ dissociation, is a prototype of the con- 
duct of all acids. Just as we may suppress the dissociation of 
phenolphthalein by raising the hydrogen ion concentration of the 
solution so may we suppress the dissociation of any acid if we can 
find a more intensely ionizing acid with which to increase the hy- 
drogen ion concentration of the solution. Similar relations hold 
for bases, and, if we regard methyl red as a base, we may illustrate 
with it the conduct of a base as we illustrated the conduct of an 
acid by means of phenolphthalein. 

Such illustrations may serve to emphasize the reason underly- 
ing the following conclusion. Whenever, in the study of a physi- 
ological process, of a step in analysis requiring pH adjustments or 
of any case involving equilibria comparable with those mentioned 
above, there is sought the effect of the pH of the solution, it may 
be expected that no particularly profound effect will be observed 
beyond a certain zone of pH. Within or at the borders of such a 
zone the larger effects will be observed. From this we may con- 
clude that the methods of determining hydrogen ion concentra- 
tions should meet two classes of requirements. In the first place, 
when the phenomenon under investigation or control involves an 
equilibrium which is seriously affected by the pH of the solution, 
the method of determining pH values should be the most accurate 
available. In the second place, when the equilibrium is held prac- 
tically constant over a wide range of pH, an approximate deter- 
mination of pH is sufficient and refinement may be only a waste 
of time. 

Neglecting certain considerations which often have to enter into 
a choice of methods it may be said that the electrometric method 
had best be applied in the first case and the indicator method in 
the second. When the nature of the process is not known, and it 
therefore becomes impossible to tell a priori which method is to be 
chosen, the colorimetric method becomes a means of exploration 
and the electrometric method a means of confirmation. 

Exception will be taken to this statement as comprehensive 
for there are cases where one or the other method has to be 






306 THE DETERMINATION OF HYDROGEN IONS 

discarded because of the nature of the solution under examina- 
tion. Nevertheless, in general, the utility of the colorimetric 
method lies in its availability where approximations are needed and 
exact determinations are useless and also in its value for recon- 
naissance; while the value of the electrometric method lies in its 
relative precision. 

In some instances the qualitative and quantitative relations of 
a phenomenon to pH should be carefully distinguished. Note, for 
instance, the significance of an optimum or characterizing point. 
Consider the conduct of phenol red and of cresol red. These two 
indicators appear to a casual observer to be very much alike in 
color and each exhibits a similar virage in buffer solutions of pH 
7.6, 7.8, etc. Careful study, however, shows that each point on 
the dissociation curve of phenol red lies at a lower pH than the cor- 
responding point on the dissociation curve of cresol red. If the 
half transformation point be taken as characteristic it may be 
used to identify these two indicators. Likewise it is the dissocia- 
tion constant of an acid or a base, the isoelectric point of a protein, 
the optimum pH for acid agglutination of bacteria, or an optimum 
for a process such as enzyme activity that furnishes characteristic 
data. 

When there is observed a correlation between pH and some effect, 
the mere determination of pH alone will of course throw but little 
light upon the real nature of the phenomenon except in rare in- 
stances. Determination of the hydrogen ion concentration will 
not even distinguish whether a given effect is influenced by the 
hydrogen or the hydroxyl ions, nor will it always reveal whether 
the influence observed is direct or indirect. It is true, however, 
that, even when the hydrogen ion concentration is effective 
through remote channels, it may be very important. Therefore 
advantage should be taken of the comparative ease with which the 
concentration of hydrogen ions may be determined or controlled 
and its influence known or made a constant during the study of 
any other factor which may influence a process. From this 
point of view methods of determining hydrogen ion concentration 
take their place beside thermometers, and buffer mixtures beside 
thermostats. 

Indeed it may be said that the failure to take advantage of 
buffers is still a prolific source of error in the experimental work 



APPLICATIONS 307 

of every branch of science having to do with solutions. In one 
case the neglect is gross; in another case it may be a perfectly 
excusable misjudgment. A complete understanding of the 
effects of the hydrogen or hydroxyl ion is very far from attainment 
and those who faithfully control the pH of their solutions are 
often rewarded by the most surprising results. To emphasize 
this aspect we may call attention to the fact that while the disso- 
ciation of glucose is quite negligible in the region of pH 7 so far 
as any appreciable effect upon the displacement of other acid- 
base equilibria is concerned, the converse proposition is decidedly 
not negligible. A shift in pH from 7.0 to 7.4 has a very marked 
influence upon the conduct of glucose in heated solutions as every 
media maker knows. Nor may it be forgotten that there are many 
compounds only the main dissociation constants of which have 
been determined; until we know the values of secondary acidic 
or basic dissociations, we have not a complete description upon 
which to base judgment of the conduct of such compounds in 
relation to pH. 

It is the opinion of the author that altogether too much em- 
phasis has been placed upon the so-called "neutral point." The 
relation [H + ] [OH] = K w holds all along the scale. The equality 
[H + ] = [OH] or pH = pOH occurs at pH 7. This is a convenient 
reference point and has been seized upon as the point of division 
in our habitual ideas of "acidity" and "alkalinity." But 
pH 7 is not used as the end point in titrations, it is not the neutral 
point in the conduct of ampholytes or selectively adsorbing ma- 
terial, and seldom is anything unique seen to happen when in a 
series of experiments a solution "crosses the line." 

Living cells are dependent upon the maintenance of a strictly 
limited hydrogen ion concentration in their environment. The 
recognition of this as a fact, independently of any theory whatever 
regarding the channels of influence, has brought hydrogen ion 
methods into the culture laboratory and into the garden. Accus- 
tomed as we are to dealing with ponderable quantities of material 
we are sometimes startled by the fact. that a cell is dependent 
upon the maintenance of an environment varying between the 
limits 0.000,001 and 0.000,000,01 gram hydrogen ions per liter. 
Sometimes the permissible limits are even closer but the order of 
magnitude remains the same. Such values, however, do not 



308 THE DETERMINATION OF HYDROGEN IONS 

represent entities separable from the other material present in 
solution. They represent only a position of balance among rela- 
tively large quantities of material containing a reserve of potential 
hydrogen ions. 

Now that N, the number of molecules of solute present per 
litre in a molar solution, is accurately known (Millikan), it is 
certain that even in a solution having a hydrogen ion normality 
as low as 10 -13 there are about 10 10 hydrogen ions per litre. This 
estimate, when taken in conjunction with the electrical charge 
associated with each ion, may indicate how it is that a normality 
of 10 -13 H + may be detected. 

But there still remains the fact that this normality is very low 
in comparison with the other material present even in distilled 
water. In solutions heavily buffered at pH 13 we find the hydro- 
gen electrode or an acid indicator rigidly stabilized in its conduct 
and it is questioned whether this can be brought about by such 
extreme relative dilutions of the hydrogen ions alone. Keller 
(1921) has expressed doubt of another sort. He calls attention 
to the diminutive size of the hydrogen ion (allowing for hydration) 
compared with a giant protein molecule, and, picturesquely pro- 
portioning the one to the other as a bacterium to a Mont Blanc, 
he questions the influence upon the protein which is attributed 
to the hydrogen ion. 

All these are "sharp-toothed questions" which, were they 
"baited with more skill, needs must catch the answer." In many 
of the answers given, however, there lies an easily detected fallacy. 
Our present convenient modes of formulating relations are regarded 
as complete pictures of the physical facts and as such are followed 
to the bitter end with disastrous results. In a previous chapter 
we have attempted to broaden the outlook just a little, and have 
suggested that in many cases a more complete formulation of 
relations would show that as the physical effectiveness of one ion 
fades out at extreme dilution other components of the solution 
maintain the continuity. From this point of view even the more 
extreme "calculation values" retain a definite significance. 

In like manner an extreme hydrogen ion concentration may be 
significant as an index of the state of an equilibrium with which 
the hydrogen ion itself has little actual physical significance. Its 
introduction as a component of the equilibrium is a convenient 



APPLICATIONS 309 

and at the same time a stoichiometrically true and mathemati- 
cally correct mode of expression containing no implications re- 
garding the actual physical effectiveness of a small hydrogen ion 
concentration as an individual quantity separable from the other 
components of a solution. At higher concentrations there can 
be little doubt of the physical effectiveness of the hydrogen ions 
whatever their size, or energy relative to other bodies. The 
energy placed on the grid of an electron tube may be small, but 
the potential of the grid may determine a large flow of energy 
between filament and plate. The hydrogen ions in a solution 
may be small in relative size or relative numbers, but they may 
control the mobilization of a large reserve. If one seeks to go 
further, perhaps to formulate a more fundamental basis, he still 
has to conform to the experimental data at hand. 

These data are too extensive, too detailed and altogether too 
complete to admit any doubt of the pragmatic value of those 
measurements we now customarily express in terms of hydrogen 
ion concentration or activity. Such values do indicate definite 
positions of equilibrium among important components of a solu- 
tion and they have oriented relations hitherto unsuspected. But 
it is by no means certain that we have attained the ultimate con- 
ception of what our measurements represent in terms of mechan- 
isms. Better descriptions of these we eagerly await. Scientific 
thought pauses where it is convenient and leaps forward when 
necessity demands; but experimental measurements remain with 
whatever force skill, scope and instrumental precision give them — 
requiring only reinterpretation with the enlargement of vision. 

In a crude way we have attempted in a previous chapter to 
give a generalized picture of oxidation-reduction relations. Here 
we encounter definite experimental facts which it is sometimes 
convenient to express in terms of "calculation values." It may 
now fairly be asked whether these are not significant as indices 
of equilibria of as much importance to the delicate adjustments 
of life processes as are hydrogen ion concentrations. If the 
studies so far made are prophetic there will be found not only 
a profound interrelationship between hydrogen ion concentrations 
and oxidation-reduction equilibria but also direct control of cer- 
tain biological processes by the reduction potential of the medium. 
See Gillespie (1920), Clark (1920) and Clark and Cohen (1922) 



310 THE DETERMINATION OF HYDROGEN IONS 

for some applications in bacteriology. See also -Chapters XVI 
and XX. 

Adsorption. Hydrogen and hydroxyl ions are particularly 
subject to adsorption upon surfaces. Since the relative activi- 
ties of these ions are especially easy to measure, methods of de- 
termining pH are of great value for adsorption studies. For a 
review of recent work see Michaelis (1922). 

References. Lachs-Michaelis (1911), Loffler-Spiro (1919), 
Michaelis (1922), Michaelis-Rona (1910, 1919, 1920), Rona- 
Michaelis (1919, 1920), Tanner (1922). 

Analyses. The empiricism that characterized the develop- 
ment of analytical methods in the hands of Fresenius and others 
left specifications for the use of mixtures of acids, such as acetic, 
and their alkaline salts in many separations. These we now know 
control the hydrogen ion concentration. Here and there in the 
special literature are to be found the calculated hydrogen ion con- 
centrations in such cases and in other cases directions which are 
somewhat more precise than the customary "slightly acid" or 
"slightly alkaline." More recently there has been undertaken 
direct experimentation with hydrogen electrode or indicator meth- 
ods. The need of further development was voiced some years ago 
by Dr. Hillebrand of the Bureau of Standards when he indicated 
to the Washington Chemical Society the need of a systematic in- 
vestigation of all analytical methods. One type of information 
urgently needed may be learned from the papers of Blum, of Fales 
and Ware and of Hildebrand. Colorimetric pH measurements on 
carbonate equilibria are furnishing valuable information in several 
simple analytical methods. Kolthoff is working on the relation of 
pH to certain oxidation-reduction titrations. Many qualitative 
color reactions remain to be studied. 

References. Anger (1921), Behrend (1893), Bishop-Kittredge- 
Hildebrand (1922), Bogue (1922), Bottger (1897), Br0nsted (1911), 
Blum (1913, 1914, 1916), Eastman-Hildebrand (1914), Fales- 
Ware (1919), Garard-Sherman (1918), Haas (1916), Hanzlik 
(1920), Haskins-Osgood (1920), Hildebrand (1913), Hildebrand- 
Bowers (1916), Hildebrand-Harned (1912), Hopkins (1921), 
Kober-Haw (1916), Kober-Sugiura (1913), Kolthoff (1919-1921), 
Kolthoff-Volgelenzang (1921), Koritschoner-Morgenstern (1919), 
Kramer-Green (1921), Kramer-Tisdale (1921), Liempt (1920), 



APPLICATIONS 311 

Lizius (1921), Marriott (1916), Mattick- Williams (1921), Menten 
(1920), Oettingen (1900), . Osterhout (1918), Robinson 
(1919, 1922) Robinson-Bahdemer (1922), Shohl (1922), 
Sollmann (1920), Swanson-Tague (1919), Tague (1920), Till- 
mans-Bohrmann (1921), Tizard-Whiston (1920), Zoller (1920). 

Autolysis of tissue is governed by the activity of enzymes 
which are sensitive to the concentration of hydrogen ions. As the 
resultant of the activity of two types of enzymes (Dernby) auto- 
lysis is controlled by the pH which brings into play the activity of 
each. 

References. Bradley (1916), Bradley-Felsher (1920), Bradley- 
Taylor (1916), Dernby (1917-1918), Gibson-Umbreit-Bradley 
(1921), Koehler-Severinghaus-Bradley (1922), Morse, M. (1916- 
1917). 

Bacteriology. A review of the applications in bacteriology 
up to 1917 is given by Clark and Lubs (1917). 

Adjustment of the reaction of media by the old titrimetric proce- 
dure was criticised by Clark (1915), and, on the introduction of suit- 
able indicators and the evidence for the advantage of adjusting 
on the pH basis, the titrimetric method has been abandoned for 
more significant and easier modern methods. Studies on growth 
optima (which see below) have shown that for the cultivation of 
most saprophytes approximate indicator control without the use 
of standards is sufficient (see Chapter VIII) . For special purposes 
and especially for the study of certain important pathogens it is 
well to adjust with the precision attained with standards. Seldom 
is electrometric control necessary. 

References. Adam (1921), Baldwin (1919), Barthel (1918-20), 
(1920), Bovie (1915), Clark (1915), Clark-Lubs (1916), Conn 
(1919), Cox-Wood (1920), Davis (1920), Dernby (1919), Fennei- 
Fisher (1919), Foster-Randall (1921), Graoe-Highberger (1920), 
Henderson-Webster (1907), Hurwitz-Meyer-Ostenberg (1915— 
1916), Jones (1919), Kligler (1917-1918), Kligler-Defandorf (1918), 
Ktister (1921), Mclntosh-Smart (1920), Massink (1921), Medical 
Research Committee (1919), Michaelis (1921), Norton (1919), 
Ponselle (1920), Reitstotter (1920), Stickdorn (1922), Wolf- 
Shunk (1921). 

The optimal zones and the limits of growth and general metabolism 
have naturally been the chief interest in the first surveys of the 



312 THE DETERMINATION OF HYDROGEN IONS 

influence of hydrogen ion concentration upon bacterial activity. 
It is now clear that in the future more exact studies will have to 
differentiate between optimal initial pH, optimal zones of growth, 
optimal zones for general or special metabolism, optimal zones 
for preservation, etc. The self limitation of acid fermentation, 
first clearly defined by Michaelis and Marcora (1912), has been 
applied to certain practical tests; for example see Clark (1915), 
Avery and Cullen (1919). pH limits for special organisms which 
have commercial significance are exemplified by control of "rope" 
in bread (Cohn-Walbach-Henderson-Cathcart) and "scab" on 
potatoes (Gillespie-Hurst). 

References. Adam (1921), Allen (1919), Avery-Cullen (1919), 
Ayers (1916), Ayers-Johnson-Davis (1918), Barthel (1918), 
Barthel-Sandberg (1919), Beckwith (1920), Bengtson (1922), 
Boas (1920), Boas-Leberle (1918), Brown-Orcutt (1920), Bunker 
(1919), Chambers (1920), Cheplin-Rettger (1920), Clark (1915- 
18) Clark-Lubs (1915-1917), Cohen-Clark (1919), Cohn-Wal- 
bach-Henderson-Cathcart (1918), Cole-Onslow (1916), Cole- 
Lloyd (1917), Colebrook (1920), Cullen-Chesney (1918), v. Dam 
(1918), Dernby, (1921), Dernby-Avery (1918), Dernby-Blanc 
(1921), De Kruif (1922), Duggar-Severy-Schmitz (1917), Erick- 
son-Albert (1922), Euler-Emberg (1919), Euler-Heintze (1919), 
Evans (1918), Foster (1920-1921), Freear-Venn (1920), Fred- 
Davenport (1918), Frothingham (1917-1918), Gainey (1918), 
Gates (1919), Gillespie (1918), Gillespie-Hurst (1918), Grace- 
Highberger (1920), Hagglund (1915), Hall-Fraser (1921-1922), 
Henderson (1918), Holm-Sherman (1921-1922), Huddleson (1921), 
Itano (1916), Itano-Neill (1919), Itano-Neill-Garvey (1920), 
Johannessohn (1912), Johansen (1920), Jones (1920), Kiesel 
(1913), Kligler (1918), Kligler-Robertson (1922), Kohman (1919), 
Kniep (1906), Lazarus (1908), Levine (1920), Lord (1919), 
Lord-Nye (1919), Lloyd (1916), Luers (1914), Meacham (1918), 
Mellon (1921), Meyerhof (1916-1917), Michaelis-Marcora (1912), 
Scheer (1921), Schoenholz-Meyer (1919-1921), Shaw-Mackenzie 
(1918), Sherman (1921), Shohl-Janney (1917), Somogyi (1921), 
Steinberg (1919), Svanberg (1918-21), Swartz (1920) Swartz- 
Shohl-Davis (1921), Waksman (1918), Waksman-Joffe (1920- 
21), Williams-Povitzky (1921), Winslow-Kligler-Rothberg (1919) 
Wolf (1918), Wolf-Foster (1921) Wolf-Harris (1917), Wolf- 



APPLICATIONS 313 

Shunk (1921), Wolf-Telfer (1917), Wright (1917), Zeller-Schmitz 
(1919). 

The influence of pH upon bacterial metabolism. The reaction 
of the medium even within the zone of optimal bacterial growth 
is found to influence either the rate, or the relative rate of specific 
types of metabolism. Not only the activity but also the pro- 
duction of enzymes is influenced and the production of special 
products such as toxins is partially controlled by the pH of the 
medium. 

References.. Arzberger-Peterson-Fred (1920), Avery-Cullen 
(1920), Atkin (1911), Barthel (1921), Barthel-Bengtsson (1920), 
Barthel-Sandberg (1920), Blanc-Pozerski (1920), Boas (1919), 
Bronfenbrenner-Schlesinger (1918), Brooks (1921), Bunker (1919), 
Charpentier (1921), Clark (1920), Cook-Mix-Culvyhouse (1921), 
Davis (1918, 1920), Dernby-Aleander (1921), Dernby-Blanc 
(1921), Dernby-David (1921), Euler-Blix (1919), Euler-Emberg 
(1919), Euler-Hammarsten (1916), Euler-Svanberg (1918, 1919), 
Fred-Peterson (1920), Gaarder-Hagem (1920-1921), Green (1918), 
Groer (1912) Gustafson (1920), Itano (1916), Jacoby (1918), 
Jones (1920), Lord-Nye (1919), Meyerhof (1917), Neuberg-Hirsch 
(1919), Northrop-Ash-Senior (1919), Patty (1921), Peterson- 
Fred-Verhulst (1921), Robinson-Meader (1920), Sasaki (1917), 
Stevens-Koser (1920), Venn (1920), Waksman-Joffe (1921), 
Wolf (1920), Wyeth (1919). 

Disinfectant action of acids and bases is certainly in large meas- 
ure a function of hydrogen or hydroxyl ion concentration; but 
specific effects of certain acids and bases, which were suspected 
before, have now been more clearly demonstrated by the use of 
hydrogen ion methods. With the conductivity method Winslow 
and Lochridge were able to show the effect of the hydrogen ion 
in simple solutions and predicted relations which more powerful 
methods have extended to complex media. 

Cohen (1922) has reviewed certain relations between pH and 
viability of bacteria under sub-lethal conditions. Time, tempera- 
ture, and pH are now linked as controlling factors in canning. 

The more direct action of hydrogen ion concentration upon 
cells must be distinguished from its control upon the effective 
state of a toxic compound. Knowledge of pH effects is therefore 
essential to the assay of disinfectants and to the advancement of 
chemotherapy. 






314 THE DETERMINATION OF HYDROGEN IONS 

References. Aubel (1920), Bettinger-Delaval (1920), Bial 
(1902), Bigelow (1921), Bigelow-Cathcart (1921), Bigelow-Esty 
(1920), Browning-Gulbransen (1921), Browning-Gulbransen- 
Kennaway (1919), Clark, J. F. (1899), Clark-Lubs (1917), Cohen 
(1922), Cohen-Clark (1919), Donk (1920), Friedenthal (1919), 
Kronig-Paul (1897), McClelland-Waas (1922), Mliller (1921), 
Neilson-Meyer (1921), Norton-Hsu (1916), Paul-Birstein-Reuss 
(1910), Paul-Kr6nig (1896), Rideal-Evans (1921), Shohl-Deming 
(1921), Tawara (1921), .Traube-Somogyi (1921), Vermast (1921), 
Waterman (1915), Weiss (1921), Winslow-Lochridge (1906), 
Wolf-Foster (1921), Wright (1917). See also "Pharmacology." 

Acid agglutination of bacteria, first definitely recognized by 
Michaelis (1911) in its relation to hydrogen ion concentration, has 
been found to be of some diagnostic use. The discovery by Ark- 
wright of separately agglutinable constituents opened up some 
investigations of possibly wide bearing. Buchanan has indicated 
some of the possible relations to serum agglutination. 

References. Arkwright (1914), Bach (1920), Barendrecht 
(1901), Bechhold (1904), Beintker (1912), Beniasch (1912), 
Bergey (1912), Bondorf (1917), Buchanan (1919), De Kruif 
(1922), Eisenberg (1919), (contains review and bibliography), 
Field-Teague (1907), Georgi (1919) Gieszczykiewicz (1916), 
Gillespie (1914), Grote (1913-1914), Heimann (1913), Jaffe" 
(1912), Kemper (1916), Krumwiede-Pratt (1913), Tiess (1919), 
Markl (1915), Michaelis (1911, 1915, 1917), Michaelis-Adler 
(1914), Murray (1918), Poppe (1912), Radsma (1919), Schidor- 
sky-Reim (1912), Sears (1913), Sgalitzer (1913), Tulloch (1914). 

d'Herelle 'phenomenon. Gratia (1921). 

Cell interior. Angerer (1920). 

Testing fermentation. See various references under other head- 
ings and especially Baker (1922), Chesney (1922), Clark (1915- 
17), Clark-Lubs (1917), Laybourn (1920), Nichols-Wood (1922). 

Balloelectricity. 

Reference. Christiansen-Christiansen (1919). 

Beer. As originally outlined by Pasteur the "reaction" of 
wort has much to do with the brewing of beer. The control of 
"disease" and of the protein material held in solution is to some 
extent dependent upon pH as are the activities of the enzymes 
concerned at each stage. 



APPLICATIONS 315 

References. Adler (1915, 1916), Emslander (1914-1919), 
Leberle-Liiers>(1914), Liiers(1914),Liiers-Adler (1915), Schjerning 
(1913). See also "Bacteriology," "Enzymes" and "Proteins." 

Blood. The hydrogen ion concentration of the blood, while 
varying slightly among normal individuals, is regulated with 
remarkable constancy in any one individual in a normal environ- 
ment. It never varies far from pH 7.4. Van Slyke »(1921), 
places the normal variation between about 7.3 and 7.5 and the 
limits compatible with life at approximately 7.0 and 7.8. Since 
the bicarbonate-carbonic acid equilibrium is one of the most 
important in the regulation of the blood's reaction it is convenient 
to define the system in terms of this equilibrium. See " carbonate 
equilibrium" for the derivation of the relation 

P H = pK 1 + log [H ^° J 



[free. COd 



Inspection of the relations involving the carbonate ion CO 3 
(see page 320) will show that at pH 7.4 [CO3] may be neglected 
and the fixed carbon dioxid may be regarded as entirely bicar- 
bonate. The extent of the bicarbonate dissociation is in doubt 
but if we substitute [BHCO3], for [HC0 3 ] where B represents any 
monovalent base, and modify pKi to accord with the experimental 
conditions, we have 

pH = 6.1 + log [BHC ° 3] 



[free C0 2 ] 

[BHCO3J -20 

The ratio - -p^r--, determines pH. Normally it is about— . 

[freeC0 2 J • 1 

From one point of view the blood may be regarded as a scav- 
enger, burning the waste products in the tissues it perfuses, and 
carrying off the final products of combustion of which C0 2 is one 
of the most important for the acid-base equilibria under con- 
sideration. With a given content of buffer in the blood the 
hydrogen ion concentration would be maintained constant under 
this inflow of C0 2 by the maintenance of a constant C0 2 pressure 
in the lungs; but with varying buffer content the hydrogen ion 
concentration could only be maintained constant by a mechan- 
ism directly responsive to hydrogen ion concentration and ca- 
pable of altering the C0 2 pressure. It seems that the respiratory 



316 THE DETERMINATION OF HYDROGEN IONS 

centre is thus directly responsive to the hydrogen ion concentra- 
tion and by its regulation of the breathing maintains in the 
alveolar air that level of C0 2 pressure which is in harmony with 
the equilibria centered about constant pH under varying condi- 
tions. Of this Haldane says: "The respiratory centre is enor- 
mously more delicate as an index of change in hydrogen ion con- 
centration of the blood than any existing physical or chemical 
method." Clinical methods based on the measurement of the 
alveolar C0 2 tension are now extensively used (see Van Slyke). 
On the other hand, the C0 2 tension is but one item of a compli- 
cated set of equilibria. It often becomes of importance to know 
the relative proportions of the other constituents of the acid- 
base equilibria. In pathological conditions the oxidative proc- 
esses may be at fault and the carbonate equilibria must be 
adjusted to accommodate the products of incomplete combustion 
in the effort of the body to maintain constant hydrogen ion 
concentration in the blood. Therefore it becomes important to 
learn the relation of the C0 2 content to the alkaline reserve. 
When this is done by gas chain or indicator titrations the hydro- / 
gen electrode and indicator methods again enter the subject 
from which they were to some extent displaced when it was found 
that there was no particular object in studying a constant main- 
tained physiologically with a degree of precision often beyond 
the precision of experimental measurement. 

Although it is convenient to express the acid-base equilibria 
of the blood in terms of the bicarbonate system other equilibria 
are of equal importance to a complete description of the mechan- 
isms. In the plasma are other substances beside the carbonic 
acid and bicarbonate which participate in the acid-base equilib- 
rium; but the most interesting relations are found in the Donnan 
equilibrium (see page 328) between the solutes of the plasma and 
the material trapped within the membranes of the blood cells. 
Of this material the blood pigment is the most important. When 
oxidized (as oxyhemoglobin) it is more strongly acidic than 
when reduced (as hemoglobin). The direct consequence is 
this: when the blood pigment gives up oxygen to the tissues the 
blood assumes more basic properties as a whole and is thus able 
to take up more C0 2 for a given displacement of pH. The 
converse change occurs on oxidation in the lungs, and tends to 



APPLICATIONS 317 

displace CO2. In this sense the blood pigment is a carrier of C0 2 
as well as a carrier of oxygen. 

Intimately connected with the regulation of the hydrogen ion 
concentration of the blood are the functions of the kidneys (see 
Cushny). By their action there are eliminated the non-volatile 
products of metabolism, several of which are of great importance 
for the acid-base equilibria of the blood. The colorimetric deter- 
mination of the pH of the urine is a comparatively simple pro- 
cedure which furnishes valuable data when properly connected 
with other data. (See for instance Blatherwick, and the works 
of Henderson, of Palmer and of Van Slyke.) 

While the greatest interest has centered in the subjects briefly 
mentioned above, there remain innumerable other problems of 
importance. Of these there may be mentioned the relation of 
the pH of the blood to the calcium-carrying power, to the activity 
of various enzymes, to the permeabilities of tissue membranes, to 
the activity of leucocytes, and to various reactions used in the 
serum diagnosis of disease. 

The student, if bewildered by the array of references given 
below, will find it profitable to read the classic work of Hender- 
son, Das Gleichgewicht zwischen Basen und Sduren im tierischen 
Organismus. By following the papers of Van Slyke and his co- 
workers the student will find reviews of various aspects of the 
subject. The respiration phase so far as the older work is con- 
cerned will be found in Barcroft's monograph. The later work 
which includes the effects of pH is reviewed by Bayliss, Hender- 
son, Parsons and others. Van Slyke's The Carbon Dioxide Carriers 
of the Blood (1921) reviews the acid-base equilibria of the carbonate 
in its relation to the acid-base equilibria of the hemoglobin, phos- 
phate, etc. 

References on acid-base equilibria of blood and related mechanisms. 
See also " Urine." 

1898 — Bugarszky-Tangl, Spiro-Pemsel. 

1900— Hober. 

1901— Rhorer. 

1902— Friedenthal, Hober. 

1903 — Auerbach-Friedenthal, Farkas, Farkas-Scipiades, 
Fraenckel, Friedenthal, Hober, Hober-Jankowsky. 

1904— Friedenthal. 



318 THE DETERMINATION OF HYDROGEN IONS 

1905— Foa, Pfaundler. 

1906— Abel-Fiirth, Benedict, Szili. 
1907 — Aggazzotti. 

1908 — Henderson, Henderson-Spiro, Spiro-Henderson. 

1909 — Hendnrson, Michaelis-Rona, Ringer, Robertson, Szili. 

1910 — Hober, Kreibich, Robertson. 

1911 — Adler-Blake, Bottazzi, Hasselbalch-Lindhard, Lob, Po- 
lanyi, Schwartz-Lemberger, Skramlik, Winterstein. 

1912 — Hasselbalch, Hasselblach-Lundsgaard, Lundsgaard, Mi- 
chaelis-Davidoff, Quagliariello-Agostino, Quagliariello, Roily, 
Salge, Sellards. 

1913 — Elias-Kolb, Henderson-Palmer, Konikoff, Masel, New- 
burgh-Palmer-Henderson, Palmer-Henderson, Rona-Gyorgy, 
Rona-Takahashi, Salge, Snapper. 

1914 — Barcroft, Blatherwick, Michaelis, Peabody, Peters, 
Roily. 

1915 — Begun-Herrmann-Munzer, Hasselbalch-Gammeltoft, 
Henderson-Palmer, Levy-Rowntree-Marriott, Ma. de Corral, 
Menten-Crile, Milroy, Momose, Palmer-Henderson, Poulton, 
Wilson-Stearns-Thurlow, Winterstein. 

1916— Gettler-Baker, Haldane, Hasselbalch-Lindhard, How- 
land-Marriott, Hurwitz-Lucas, Levy-Rowntree, Marriott, Mc- 
Clendon, McClendon-Magoon, Macleod, Reemlin-Isaacs, 
Rona-Ylppo, Scott, Ylppo. 

1917— Bienstock-Czaki, Cullen, Fitz-Van Slyke, Hasselbalch, 
Henderson, Hober, Hooker-Wilson-Connet, Isaacs, McClendon- 
Shedlov-Thomson, Milroy, Palmer-Van Slyke, Parsons, Peters, 
Scott, Stillman-Van Slyke-Cullen-Fitz, Van Slyke, Van Slyke- 
Cullen, Van Slyke-Stillman-Cullen. 

1918— Bayliss, Goto, ■ Hasselbalch-Warburg, Henderson- 
Haggard, Macleod, Macleod-Knapp, Sonne-Jarlov, Straub- 
Meier, Zunz. 

1919— Debenham-Poulton, Donegan-Parsons, Haggard-Hender- 
son, Haskins, Irwin, Macleod, Parsons, Schloss-Harrington, Van 
Slyke-Stillman-Cullen, Van Slyke-Austin-Cullen. 

1920— Anon, Bayliss, Bisgaard-N0rvig, Blatherwick, Campbell- 
Poulton, Collip, Collip-Backus, Coulter, Dale-Evans, Davies-Hal- 
dane-Kennaway, Dragstedt, Forbes-Halverson-Schulz, Fredericia, 
Grant, Goldman, Parsons, Haggard-Henderson, Hartridge, Haskins- 



APPLICATIONS 319 

Osgood, Henderson, L., Henderson, Y., Henderson-Haggard- 
Coburn, Hills, Joffe-Poulton, v. Kapff, MacNider, Mellanby- 
Thomas, Menten, Michaelis, Moore, Parsons, Parsons-Parsons, 
Parsons-Parsons-Barcroft, Parsons-Shearer, Prentice-Lund-Harbo, 
Priestley, Raymund, Reimann, Rieger, Suitsu, Van Slyke- 
Palmer. 

1921 — Barr-Peters, Bazett-Haldane, Busa, Chistoni, Collip, 
Doisy-Eaton, Evans, C. L., Fleisch, Gauss, Haggard-Henderson, 
Haldane, Hastings-Murray-Murray, Henderson, Hill, Jarloev, 
Ma. de Corral, Means-Bock- Woodwell, Meier-Kronig, Parsons- 
Parsons, Peters-Barr, Peters-Barr-Rule, Reimann-Reimann, 
Reimann-Sauter, Roaf, Smith-Means-Woodwell, Trevan-Boock, 
Van Slyke, Van Slyke-Stadie, Winterstein. 

1922 — Barach-Means-Woodwell, Barkan-Broemser-Hahn, Cul- 
len, Coulter, Doisy-Briggs-Chouke, Henderson, Hirsch-Peters, 
Hirsch- Williams, Macleod, Parsons-Parsons, Williams-Swett. 

Bread. In the baking of bread it is essential that the proteins, 
such as glutin, which are responsible for the holding of the gas, 
shall be conditioned by the proper pH. The pH may also control 
the growth of the "rope" organism. The activity of yeast and 
the evolution of CO2 from baking powders have relations to the 
pH of the dough. 

References. Bailey-Peterson (1921), Cohn-Cathcart-Hender- 
son (1918), Cohn-Henderson (1918), Cohn-Walbach-Henderson- 
Cathcart (1918), Freear-Venn (1920) Henderson (1918), Hen- 
derson-Cohn-Cathcart-Wachman-Fenn (1919), Henderson-Fenn- 
Cohn (1919), Jessen-Hansen (1911), Landenberger-Morse (1918) 
(1919), Liiers (1920), Patten (1920), Sharp-Gartner (1922), Wahl 
(1916). 

Breeding. Control of spermatozoan activity. See "Compara- 
tive and General Physiology," and C. G. L. Wolf (1921). 

Body Fluids (other than blood, urine, digestive juices, cere- 
brospinal fluid). 

References. Aggazzotti (1921), Bloomfield-Huck (1920), Collip 
(1920), Farkas-Scipjades (1903), Foa, (1905, 1906), Fraenckel 
(1905), Gies (1916), Goldberger (1917), Hertel (1921), Huddelson 
(1921), Lob-Higuchi (1910), Loeb-Atchley-Palmer (1922), Long- 
Fenger (1915, 1916), Marshall (1915), Michaelis-Kramsztyk 
(1914), Okada (1915), Quagliariello (1916-1921), Schade-Neu^ 
kirch-Halpert (1922), Shepard-Gies (1916), Uyeno (1919). 



320 



THE DETERMINATION OF HYDROGEN IONS 



Canning. The National Canners' Laboratory has so related 
time, temperature and pH that economy and certainty in the 
commercial sterilization of canned foods can be assured. 

References. Bigelow (1921), Bigelow-Cathcart (1922), Koh- 
man (1922), Rogers-Deysher-Evans (1921). 

Carbonate Equilibria. When carbon dioxid dissolves in 
water without any base to form carbonate there are presumably 
present in the water both anhydrous C0 2 and the hydrate, 
H2CO3, carbonic acid. Analytical methods do not ordinarily dis- 
tinguish these two forms, and, since the sum of the two is generally 
the more important quantity, we may write the equilibrium equa- 
tion for the relation between a partial pressure, P, of gaseous 
carbon dioxid and the dissolved carbon dioxid as follows: 

[C0 2 ] + [H 2 C0 3 ] = [free C0 2 ] = KoP 

In the presence of bases we still have the above relation holding 
tbetween the partial pressure and that portion of the total CO2 
c which remains uncombined. However, variation in the composi- 
tion of the solution will vary the magnitude of K . We probably 
make no significant error if we regard [free C0 2 ] in carbonate solu- 
tions to be influenced by the total salt (carbonate) just as it is 
influenced by the total salt concentration in a solution containing 
no base. On this basis Johnston (1915) uses Bohr's data for 
the absorption coefficients of carbon dioxid in sodium chlorid 
solutions of different concentration, and calculates therefrom 
the values of Kq in terms of molar concentration. 

Johnston's table of K 



TEMPERATURE 


IN WATER 


IN 1 . 17 M SALT 


IN 3.44M SALT 


3.5 


0.0672 


0.0484 


0.0270 


4.2 


0.0500 


0.0367 


0.0213 


16.0 


0.0441 


0.0328 


0.0193 


25.0 


0.0338 


0.0260 


0.0159 


30.0 


0.0297 


0.0232 


0.0142 


40.0 


0.0236 


0.0185 


0.0117 



From these values Johnston interpolates the following values 
of K for the indicated concentrations of total base or salt at 

1 



25°C. Included below are the values of pKo = log 



Ko' 



APPLICATIONS 



321 



TOTAL BASE 
OR SALT 


0.0 


0.1 


0.2 


0.3 


0.5 


1.0 


K 

pK„ 


0.0338 
1.471 


0.0329 
1.483 


0.0321 
1.493 


0.0314 
1.503 


0.0300 
1.523 


0.0270 
1.569 



Dissolved C0 2 reacts with water and since [H2O] may be regarded 
as constant we have the equilibrium equation 



[CQ 



[H 2 CO; 



= K , Qr [CQ 2 l + [HsCOa] = K , + x 



[H 2 C0 3 



(68) 



The H 2 C03 dissociates in steps and for the first step the equilib- 
rium condition is 



[H+] [HCQ 3 ] 
[H 2 C0 3 ] 



= K" 



69) 



Combining equations (68) and (69) and collecting constants we 
have 

[H+] [HCO3] = 
[COJ + [H 2 C0 3 ] 

or using the convention mentioned above 
[H+] [HCO3] 



[free C0 2 ] 



= Ki 



(70) 



The constant Ki is sometimes called the first dissociation con- 
stant of carbonic acid. It is not strictly so but is rather of the 
nature of an "apparent dissociation constant." Ki is more use- 
ful than the true dissociation constant but is probably much 
smaller. 

For the second stage of dissociation the equilibrium condition is: 



[H+] [CO,] 



= K 2 



(71) 



[HCO3] 

In addition to these equations there is the useful relation 
)f electrical neutrality, 

[B+] + [H+] = [HCOj + 2 [C0 3 ] + [OH] (72) 

vhere [B+] represents the total concentration of cations other than 
H + ] and all species are represented in equivalent concentrations. 



322 THE DETERMINATION OF HYDROGEN IONS 

One of the chief experimental difficulties in handling carbonate 
solutions is the control or the evaluation of P. But while this 
is susceptible to management the correct evaluation of Ki and 
K 2 is a matter of great complexity for the following reasons. If 
salts such as Na 2 C03 and NaHC0 3 are used as experimental ma- 
terial to establish various proportions of carbonate and bicarbon- 
ate ions it becomes necessary to know the degree of their dis- 
sociation at known concentrations of the salts, or if complete 
dissociation occurs it becomes necessary to know the effect of 
different concentrations upon activities. This involves the whole 
unsettled question of the conduct of "strong electrolytes." Hith- 
erto there have been carried over to pH studies the constants 
derived by the use of conductivity data which are not strictly 
applicable. 

If yi represents the degree of dissociation of NaHCC>3 and 
y 2 degree of dissociation of Na 2 C0 3 we have the following rela- 
tions according to Seyler and Lloyd (1917). 

[Na] 0.05 0.1 0.2 0.3 0.5 1.0 

y! 0.82 0.78 0.73 0.69 0.64 0.52 

y 2 0.56 0.66 0.37 0.31 0.24 0.14 

Space does not permit a detailed discussion of the above values 
and numerous other quantities which enter into the data of 
carbonate equilibria. We shall proceed with the more general 
relations indicated by the pure equilibrium equations and shall 
give without comment Johnston's values for the more important 
constants. 

Putting the equations into logarithmic form, and using for 

terms such as log ^ the expression pK, we have the following 
useful relations: 

pH = pKi + log [HC0 3 ] - log [free C0 2 ] (73) 

pH = pKi + pK + log [HCO3] - log P (74) 

pH = pK 2 + log [C0 3 ] - log [HCO3] (75) 

pH = I pK + \ pK x + \ pK 2 - \ log P + \ log [C0 3 ] (76) 

m+1 J 2X0^1^ + KpKxP [H+] + K w [H+] - [H+P 

L J [H+] 2 , 

For the values of pK see page 320. From Johnston's selected 



APPLICATIONS 



323 



values for the first and second acid dissociation constants at 
25°C. we have pKi = 6.47 and pK 2 = 10;32. For other values 
see references. 

Inspection of the combined equations will show that pH is 
denned by any two of the variables or conversely that pH and 
one variable determine the state of a carbonate equilibrium. 
By the use of equation (77) the total base can be brought into 
consideration and it can be shown that the total base and one 
variable such as pH or P will define the position of a carbonate 
equilibrium. See (77). Thus a carbonate solution exposed to the 
atmosphere with its more or less constant partial pressure of 
C0 2 at 0.0003 atmosphere will tend to reach a definite pH value 
which is determined by the total base. This may be as low as 
pH 5.0 for solutions containing very little base or as high as pH 
10 in a solution about normal with respect to [B+]. Based upon 
such relations are analytical methods for determining C0 2 par- 
tial pressures from pH and known concentrations of total base. 

Equations (73) and (74) are of importance in the study of blood 
the pH of which may be defined in terms of the ratio of bicarbonate 
to free C0 2 or in terms of bicarbonate and P. See section on 
blood. Direct experimental data for which equation (75) ex- 
presses the fundamental relations are given as follows by Auer- 
bach and Pick (1912): 



pH values for mixtures of sodium carbonate and bicarbonate at 18 C. after 
Auerbach and Pick 



MOLS PES LITRE 




MOLS PER LITHE 








pH 




pH 


' NaHCOa 


NasCOi 




NaHCOs 


Na 2 C0 3 




0.20 


0.00 


8.35 


0.10 


0.000 


8.35 


0.19 


0.01 


8.90 


0.09 


0.005 


8.98 


0.18 


0.02 


9.15 


0.08 


0.010 


9.30 


0.16 


0.04 


9.45 


0.07 


0.015 


9.50 


0.14 


0.06 • 


9.65 


0.06 


0.020 


9.60 


0.12 


0.08 


9.96 


0.05 


0.025 


9.87 


0.10 


0.10 


10.10 


0.04 


0.030 


10.05 


0.08 


0.12 


10.35 


0.03 


0.035 


10.23 


0.06 


0.14 


10.45 


0.02 


0.040 


10.35 


0.04 


0.16 


10.65 


0.01 


0.045 


10.7 


0.02 


0.18 


11.0-11.8 


0.00 


0.050 


11.4 


0.00 


0.20 


11.59 









324 THE DETERMINATION OF HYDROGEN IONS 

Equation (76) is of importance when it is desired to know 
the relations between- partial pressure of C0 2 and the state of 
some carbonate equilibrium such as that of calcium carbonate. 
In this case we have another set of relations. Calcium carbonate 
is but slightly soluble per se. In the equilibrium equation 

[Ca++] [CO,] = K 
[CaC0 3 ] 

we often have to deal with a constant value of CaC0 3 maintained 
by the presence of solid CaC0 3 . Under such circumstances we 
may combine this constant with the dissociation constant giving 

[Ca++] [C0 3 ] = K 8 (78) 

where K 8 is the "solubility product." 

By combining (78) with (76) it is seen how Ca++ can be gov- 
erned by P, a relation of geological importance. 

K 8 varies with the nature of the solid phase, (Calcite, Aragonite 
or precipitated calcium carbonate of different states of fineness). 
It is of the order of 1 X 10 -s . 

The equations of carbonate equilibria have been left in their 
more general form to show the more general relations. Modi- 
fications for special purposes are very numerous and beyond 
the scope of this sketch. For detailed treatment see references 
under "Analyses," "Blood," "Water," "Equilibria," etc. A 
treatment of the general biological importance of the carbonate 
equilibria is given in The Fitness of the Environment by Henderson. 

References. Auerbach-Pick (1912), Bjerrum-Gjaldbaek (1919), 
Frary-Nietz (1915), Henderson (1913), Henderson-Black (1908), 
Johnston (1915, 1916), Johnston-Williamson (1916), McClendon 
(1917), McClendon-Shedlov-Thomson (1917), Michaelis-Rona 
(1914), Prideaux (1915), Seyler-Lloyd (1917), Thiel-Stroheker 
(1914), Tillmans (1921), Van Slyke (1917, 1922), Wagner-Enslow 
(1922), Walker-Cormack (1900), Wilke (1921)-, Windish-Dietrich 
(1920). 

Catalysis. The catalytic activity of the hydrogen and the 
hydroxyl ions in such transformations as the hydrolysis of cane 
sugar has taken a prominent place in the development of the theory 
of electrolytic dissociation. Under limited conditions one or an- 



APPLICATIONS 325 

other of these catalytic processes is proportional to the concentra- 
tion of the hydrogen or the hydroxyl ions; but there may enter 
the action of neutral salts. The theory of their influence is now 
being recast in accord with the concept of "activity." The older 
literature on hydrogen and hydroxyl ion catalyses is reviewed 
in the monograph by Woker (1910, 1915). A few recent refer- 
ences are: Abel (1920), Akerlof (1921), Jones-Lewis (1920), Kailan 
(1920), Karlson (1921), Northrop (1921). See Enzymes, Salt 
Action and Chapter XX. 

Cerebrospinal Fluid. 

References. Bisgaard (1913), Botazzi-Craifaleanu (1916), Col- 
lip (1920), Felton-Hussey-Bayne-Jones (1917), Hertel (1921), 
Hurwitz-Tranter (1916), Levinson (1917, 1919), Meier (1921), 
Shearer-Parsons (1921), Weston (1916). 

Cheese. 

References. AUemann (1912), Barthel-Sandberg (1919), Okuda- 
Zoller (1921), van Dam (1910). 

Colloids. That the dispersion of colloids may be influenced 
by the "reaction" of the medium has long been known. So widely 
scattered is the literature on this particular phase of colloid chem- 
istry that the author has made no attempt to assemble it. It 
is through the study of protein solutions that the most distinctive 
advances have been made. Beginning with Hardy the study 
of proteins as amphoteric electrolytes has been carried forward 
by Pauli, Michaelis, Robertson, S0rensen, Henderson, Loeb and 
others until there has developed a distinct protest against the 
separation of certain of the phenomena of colloids from the appli- 
cation of the simpler relations of crystalloids. How far the matter 
nay be pushed in its application to other types of material taking 
he "colloidal state" remains to be determined. 

A very good discussion of the relation of the developments in 
>rotein chemistry to colloid chemistry is given by S0rensen (1917). 
Compare Loeb, 1922.) 

References. Abderhalden-Fodor (1920), Adolf -Pauli (1921), 
Arrhenius (1922), Bethe (1920), Clowes (1913), Ellis (1911) 
:,abes (1921), Lachs-Michaelis (1911), Lillie (1909), McBain- 
! almon (1920), McDougal-Spoehr (1919), McGuire-Falk (1922), 
: leier-Kronig (1921), Michaelis (1920, 1921, 1922), Michaelis- 
:tona (1919-1920), Ostwald (1912), Perrin (1904), Procter (1921), 



326 THE DETERMINATION OF HYDROGEN IONS 

Rona-Michaelis (1919), Schoucroum (1920), Smith (1920), 
Spiro (1916), Stiegler (1921), Varga (1919), Walpole (1914) /Will- 
iams (1920). See also "Proteins," "Adsorption," "Donnan 
Equilibrium," " Electrophoresis." 

Comparative and General Physiology. 

References. Aggazzotti (1913), Andrus (1919), Arrhenius (1921), 
Atkins (1922), Barkan-Broemser-Hahn (1922), Barratt (1905), 
Bernstein (1913), Bethe (1909), Brenner (1921), Broderick (1921), 
Burgh-Clark (1921), Burridge (1920, 21), Carr (1921), Clowes- 
Smith (1922), Cohn (1917), CoUett (1919, 1921), Collip (1920- 
1921), Coulter (1920), Cremer (1906), Crozier (1915-19), Dale 
(1913), Dale-Thacker (1914), Fletcher-Hopkins (1907), Galeotti 
(1906, 1920), Garrey (1920), Girard (1909), Goldberger (1917)/ 
Gray (1920), Hampshire (1921), E. N. Harvey (1920), R. B. 
Harvey (1920), Hastings-Murray (1921), Herbst (1904), Hirsch 
(1921), Hiruma (1917), Hober (1910), Hopkins (1921), Hurwitz 
(1910), Ivy-Oyama (1921), Jacobs (1920-22), Jameson-Atkins 
(1921), Jewell (1920), Kahlenberg (1900), Kastle (1898), Kopac- 
zewski (1914), Kfizencky (1916), Langefeldt (1921), J. Loeb, 
(1898, 1903, 1904, 1906), Loeb-Wasteneys (1911), R. Loeb (1920), 
Lloyd (1916), MacArthur (1920), McClendon (1916, 1920), 
McClendon-Mitchell (1912), MacDougall (1921), Meyerhof (1918), 
Mines (1912), Moore (1919, 1920), Moore-Roaf- Whitley 
(1905), Moore-Whitley-Webster (1921), Morse-Goldberg 
(1922), Neilson-Meyer (1921), Neugarten (1919), Oden (1916), 
Ostwald-Kuhn (1921), Parnas-Wagner (1914), Pechstein 
(1915), Philippson-Hannevart (1920), Plotho (1920), Popielski 
(1919), Porcelli-Titone (1914), Powers (1921-22), Prentice- 
Lund-Harbo (1920), Reichel (1922), Resch (1917), Richards 
(1898), Ritchie (1922), Roaf (1912-1922), Rohde (1920), Rona- 
Wilenko (1914), Roncati-Quagliariello (1921), Roth (1917), 
Saunders (1920), Schwyzer (1914), Shelford-Powers (1915), 
Shohl (1914), Straub-Meier (1919), Traube (1920), Warburg 
(1910), Wells (1915), Whitley (1905), Wolf (1921). 

Crystallography. Wherry (private communication) states 
that there is reason to believe that the pH of a medium may some- 
times control crystal form. 

Culture of organisms other than bacteria, plants and tissue. 

References. Bodine, (1921), Young-VanSant (1922). See also 



APPLICATIONS 327 

numerous notes in references under "Comparative and General 
Physiology," "Bacteriology," and "Tissue culture." 

Dakin's Solution. 

Reference. Cullen- Austin (1918). 

Digestive System. The digestive tract is primarily the chan- 
nel for the intense activity of hydrolytic enzymes and as such is 
provided with mechanisms for the establishment of hydrogen ion 
concentrations favorable to these enzymes. Hydrogen electrode 
methods have correlated the regional activity of particular en- 
zymes with the reactions there found, have clarified some of the 
differences between the digestive processes of infancy and adult 
life, aided in the explanation of the acid and alkali formation, and 
have been of service in the improvement of clinical methods for the 
assay of pepsin activity and the diagnosis of abnormal secretion 
of hydrochloric acid in the stomach. The control of specific phys- 
iological functions such as secretion of conditioning agents (see 
Bayliss, 1918), permeabilities, and activities of the varied muscu- 
lature, as well as investigations upon the condition in the digestive 
tract of substances such as calcium and phosphate which form in- 
soluble precipitates are subjects which present promising material 
for the application of modern methods. Shohl and King (1920) 
have recently reviewed and improved methods of studying 'gas- 
tric acidity. 

References. Allaria (1908), Ambard-Foa (1905), Auerbach- 
Pick (1912, 1913), Cannon (1907), Christiansen (1911, 1912, 
1921), Davidsohn (1911, 1912, 1913, 1921), Foa (1905, 1906), Fow- 
ler-Bergeim-Hawk (1915), Fraenckee (1905), Graham (1911), 
Hahn (1914), Hainiss (1921), Hammett (1922), Hess (1915), 
Hess-Scheer (1921), Howe-Hawk (1912), Huenekens (1914), 
Krummacher (1914), Lanz (1921), Long-Fenger (1917),McClendon 
(1915, 1920), McClendon-Bissell-Lowe-Meyer (1920), McClen- 
don Myers-Culligan-Gydesen (1919), McClendon-Shedlov-Thom- 
son (1917), McClendon-Shedlov-Karpman (1918), McWhorter 
(1918), Menten (1915), Michaelis (1917, 1918, 1920), Michaelis- 
Davidsohn (1910), Myers-McClendon (1920), Nelson-Williams 
(1916), Okada-Arai (1922), Popielski (1919), Rolph (1915), 
Rona-Neukirch (1912), Salge (1912), Scheer (1921), Schryver- 
3inger (1913), Shohl (1920), Shohl-King (1920), Tangl (1906), 
IYaube (1920), Ylppo (1916). 






328 



THE DETERMINATION OF HYDROGEN IONS 



Dissociation Constants as determined with the hydrogen 
electrode or indicator methods. Compare Chapter I. 

References. Agostino-Quagliariello (1912), Dernby (1916), 
Eckweiler-Noyes-Falk (1920), Eijdman (1906), Kastle (1905), 
Kolthoff (1918, 1920), Michaelis (1911, 1913, 1914), Michaelis- 
Garbendia (1914), Michaelis-Rona (1913, 1914, Prideaux (1911), 
Salm (1906, 1908), Scudder (1914), Tizard (1910), Weisse-Meyer 
Levy (1916). See Indicator constants. 

Donnan Equilibrium. Imagine a solution of a simple elec- 
trolyte and a membrane permeable to the electrolyte. Upon 
one side of the membrane let there be a solution of a substance 
which cannot penetrate the membrane but which can enter into 
the equilibrium of the simple electrolyte. A simple case is the 
following. Let the initial state be illustrated by the following 
scheme where there is placed upon one side of the membrane 
M a dilute solution of HC1 and upon the other side the acid HR 
neither the anion nor the undissociated residue of which can 
penetrate the membrane. 



[HR], 



M 



[HC1] 2 

[H+] 2 

[CI]. 



Chlorine ions (or HC1) will diffuse from right to left until, 
when equilibrium is attained, there will be the following state 



[HC1] 3 

[HR], 

[H + ] 3 

[R] 3 

[CI]. 



M 



[HC1], 

[H + ] 4 

[CI], 



If now we place hydrogen electrodes on the two sides of the 
membrane the E. M. F. of this gas chain will be determined in 
part by the relative concentrations of the hydrogen ions and in 
part by a potential difference across the membrane. This mem- 
brane potential difference we shall call E d 



E.M.F. = 5Tln|5!I 3 
nF [H+] 4 



+ E d 



We may also place on the two sides electrodes, the potential 
differences at which are determined by the relative concentrations 



APPLICATIONS 329 

of the chlorine ions (e. g. Pt-Cl electrodes or calomel electrodes). 
For such a chain we would have 

E.M.F. = — ln[2| 4 + E d 
nF [Cl] 3 

We have already specified however that the system is at equilib- 
rium. Therefore no energy could be obtained from either one 
of the chains described above. The E. M. F. in each case is 
then zero and since Ed is the same in each case 

[H+]» = [Oj* 

[H + ] 4 [a]. 

The rule of electrical neutrality indicates that on the right side 
of the membrane [H+] 4 = [Cl _ ] 4 . Combining this relation with 
the other we then have 

[H+] 4 2 = [H+] 3 [Cl] 3 

There are various directions in which we may now proceed. 
As one example let us assume the very simple case where the 
dissociations of HR and HC1 are complete, and let us further 
assume that the system is divided by the membrane into two 
equal parts. Between the initial and the final state of the sys- 
tem chlorine ions have diffused from right to left until the con- 
centration [Cl] 3 is x. Then [H+] 3 = [H+] x + x and [H+] 4 = [H+] s 
— x. Introducing these values into the foregoing equation we 
have 

([H+] 2 - x) 2 = x ([H+], + x) 



>r 



[H+] 2 - x _ [H+] 2 + [H+]i or x = [H+tf 



x [H+] 2 [H+li + 2[H+] 2 

The following table will give an idea of the magnitude of the 
effects due to the conditions assumed. 

As we have already indicated, the difference of potential be- 

ween two hydrogen electrodes placed on opposite sides of the 

) aembrane must, at the equilibrium state of the system, be equal 

; nd opposite to the potential difference at the membrane. Hence 



330 



THE DETERMINATION OF HYDROGEN IONS 



the membrane potential difference may be expressed in terms of 
a hydrogen electrode gas chain: 

RT ln [H+] 3 
F [H+]/ 

By using this relation we calculate the membrane potential 
difference given in millivolts in the last column of the following 
table. 



[Ri»-[H+], 


[H + ], 


INITIAL KATIO 

[H+J. 

[H + ], 


PER CENT HC1 
DIFFUSED TO 

ESTABLISH 
EQUILIBRIUM 


EQUILIBRIUM 
DISTRIBUTION 

[H+], 

RATIO z xr 

[H + ]4 


MEMBRANE 

POTENTIAL IN 

MILLIVOLTS 


0.01 

1.0 

1.0 


1.0 
1.0 
0.01 


0.01 
1.0 
100.0 


49.8 
33.3 
0.98 


1.01 
2.0 
101.0 


- 0.3 

- 18.0 
-120.0 



Of course the conditions assumed for purposes of illustration 
are extremely simple but they suffice to indicate the nature of 
relations of very great importance in the physiology of the living 
cell. 

References. Donnan (1911), Donnan-Harris (1911), Loeb 
(1921-22), Michaelis (1922), Moore-Roaf-Webster (1912), 
S0rensen (1917). See also "Blood," "Comparative and General 
Physiology." 

Dry-Cells. 

Reference. Haller-Ritchie (1920). 

Electroplating. The potential at which hydrogen is de- 
posited freely upon an electrode is a function of the hydrogen ion 
concentration of the solution. Therefore pH is important in 
controlling gassy deposits. In addition it is found that buffer 
solutions, maintaining the pH within definite limits, aid in the 
production of desirable qualities in nickel deposits. 

References. Bennett-Rose-Tinkler (1915), Blum (1920, 1921), 
Kiister (1900), Thompson (1922). 

Electrophoresis (Cataphoresis) and Electro-Osmosis. 
An electrically charged body placed between an anode and a 
cathode will tend to move toward the pole having a charge opposite 
in sign to the charge on the body. If the body is a simple ion, 
the movement is called ionic migration. If the body is a particle 



APPLICATIONS 331 

suspended in a medium such as water, the movement is called 
electrophoresis. More generally it is known as cataphoresis. 
The distinction between ionic migration and electrophoresis is 
not always clear in the case of material in the colloidal state. 

We shall not discuss the various theories advanced to account 
for the experimental facts but shall treat briefly only that point 
of view which it will be profitable to investigate further with 
the aid of methods for determining pH. 

Since acidic or basic ionization may determine the sign of the 
charge upon a body of amphoteric nature the sign may be a func- 
tion of the pH of the medium (aqueous). The direction of elec- 
trophoresis is then a function of pH. At the isoelectric point 
electrophoresis is a minimum. The position of this minimum on 
the pH scale is a function of the acidic and basic dissociation con- 
stants and the zone of the minimum may be narrow or broad 
according to the relative magnitudes of the constants. See 
Chapter 1. The method of electrophoresis is useful in determin- 
ing isoelectric points. 

There can be no movement such as that noted above without 
a reciprocal interaction between suspended or dissolved material 
and the dispersing medium. If then the charged particles are 
fixed in position, as in the form of a porous diaphragm, are placed 
in water and the whole subjected to a potential gradient, the 
water will tend to move (electro-osmosis). The same relative 
relations indicated above then hold. If the diaphragm is of an 
amphoteric nature the direction of water flow will depend upon 
the acidic and basic properties of the diaphragm and upon the 
pH of the aqueous phase. 

In either one of the two cases (particles fixed or free to move) 
the same end result will be obtained if the particles adsorb hydro- 
gen and hydroxyl ions according to such adsorption isotherma 
that equality of adsorption and consequently equality of elec- 
trical charge is attained at a definite pH value. On either side of 
this pH value the excess adsorption of one or the other ion will 
depend upon their concentrations which are a function of pH 
by reason of the relation [H + ] [OH - ] = K w . The position of this 
"isoelectric" point is a function of the properties of the material 
and may lie anywhere along the pH scale (according to the nature 
of the material) with a narrow or broad isoelectric zone. 



332 THE DETERMINATION OF HYDROGEN IONS 

The converse to the above propositions is that nitration pro- 
duces a potential difference across the filter which is a function 
of the acidic and basic nature of the filter and of the pH of the 
solution filtered. 

Obviously the above sketch covers restricted conditions. 

References. Barratt-Harris (1912), Briggs (1918), Freundlich 
(1921) Gyemant (1921), Michaelis (1914, 1922), Perrin (1904- 
1905), Porter (1921), Putter (1921), Steigmann (1920), Szent- 
Gyorgyi (1920, 1921), Svedberg (1916), Svedberg-Anderson 
(1919). See also "Isoelectric Point." 

Enzymes. The activity of enzymes as influenced by the hy- 
drogen ion concentration of the solution has occupied the atten- 
tion of many investigators since the publication of S0rensen's 
paper (1909). The analogy between the activity curves of several 
enzymes and the curves relating the "dissociation residues" of 
amphoteric electrolytes to pH suggested to Michaelis the ampho- 
teric nature of enzymes (cf. Loeb 1909). Northrop has shown 
important relations of activity to the acid-base nature of the 
substrate. Holderer's observations on the extraction of enzymes 
from cells with solvents of different reaction are most suggestive. 
The necessity of controlling the pH of enzyme solutions for assays 
as well as in the study of the effect of salts and in experiments 
having to do with the formulation of the laws of enzyme activity 
(Van Slyke and Cullen) is now generally recognized. Barendrecht 
in the development of his radiation theory notes the special im- 
portance of the hydrogen ions. 

The following is a rough classification of studies on specific 
enzymes. 

Amygdalase. Bertrand-Compton (1921). 

Amylase. Ambard (1921), Biederman-Rueha (1921), Euler- 
Svanberg (1921), Falk-McGuire-Blount (1919), Maestrini (1921), 
Groll (1920), McGuire-Falk (1920), Sherman (1919), Sherman- 
Thomas-Baldwin (1919), Sherman-Schlessinger (1915), Sherman- 
Thomas (1915), Sherman-Walker (1917), Sjoberg (1920), 
Takamine-Oshima (1920). 

Bacterial enzymes. Abderhalden-Fodor (1921), Avery-Cullen 
(1920), Barthel-Sandberg (1920), Blanc-Pozerski (1920), Clark 
(1920), Dernby (1917), Dernby-Blanc (1921), Groer (1912), Itano 
(1916), Kanitz (1903), Lord (1919), Meyer (1911), Nye (1922), 
Waksman(1918), West-Stevens (1921). 



APPLICATIONS 333 

Carboxylase. Neuberg (1915). 

Catalase. Bodansky (1919), Burge (1920), Euler-Blix (1919), 
Falk-McGuire-Blount (1919), Harvey (1920), Michaelis-Pechstein 
(1913, 1914), Morgulis (1921), Phragmen (1919), Senter (1905), 
S0rensen (1909), Sjoberg (1920), Waentig-Steche (1911). 

Gellase. Bertrand-Holderer (1910). 

"Diastases" (Important historical references) Fernbach (1906), 
Fernbach-Hubert (1900). 

Filtration of. Holderer. 

Glycogenase. Norris (1913). 

Coferments. Biederman (1921), Tholin (1921). 

Emulsin. Bayliss (1912), Nordefeldt (1921), Vulquin (1910). 
Willstatter-Csanyi (1921). 

Erepsin. Euler (1907), Dernby (1916), Rona-Arnheim (1913). 

Esterases (lipase). Avery-Cullen (1920), Baur (1909), David- 
sohn (1912-1913), Falk, I. (1918), Falk, K. (1916), Groll (1920), 
Haley-Lyman (1921), Hulton-Frankel (1917), Kastle (1902), 
Rona (1911), Rona-Bien (1914), Rona-Reinicke (1921), Rona- 
Michaelis(1911). 

Invertase. Bertrand-Rosenblatt-Rosenblatt (1912), Euler 
(1921), Euler-Laurin (1919, 1920), Euler-Svanberg (1918-21), 
Fales-Nelson (1915), Falk-McGuire (1921), Fodor (1921), Griffin- 
Nelson (1916), Hudson (1910), Hudson-Paine (1910), Kanitz 
(1911), Langefeldt (1921), Michaelis (1921), Michaelis-Davidsohn 
(1911), Michaelis-Menten (1913), Michaelis-Pechstein (1914), 
Michaelis-Rothstein (1920), Nelson-Griffin (1916), Nelson-Hitch- 
cock (1921), Nelson-Vosburgh (1917), Rona-Bach (1921), Rona- 
Bloch (1921), Sjoberg (1921), S0rensen (1909), Vosburgh (1921). 

Lactase. Davidsohn (1913). 

Levanase. Kopeloff-Kopeloff-Welcome (1920). 

Maltase. Adler (1916), Kopaczewski (1912, 1914, 1915), 
Michaelis-Rona (1913, 1914), Rona-Michaelis (1913). 

Oxidases, etc. Bunzel (1915), Bunzell (1916, 1917), Ohlsson 
(1921), Menten (1919, 1920), Reed (1916), Rose-Kraybill-Rose 
(1920). 

Oxynitrilase. Krieble-Wieland (1921). 

Pectase. Euler-Svanberg (1919). 

Optimum temperature. Compton (1915, 1921). Euler-Laurin 
(1920). • ' 



334 THE DETERMINATION OF HYDROGEN IONS 

Papain. Frankel (1917). Chesnut (1920). 

Peroxidase. Bouma-Van Dam (1918). 

Pepsin. Christiansen (1912), Van Dam (1915), Davidsohn 
(1912), Funk-Niemann (1910), Gies (1902), Graber (1921), 
Groll (1920), Gyemant (1920), Loeb (1909), Michaelis (1918), 
Michaelis-Mendelsohn (1914), Michaelis-Rothstein (1920), North- 
rop (1919, 1920, 1921), Okada (1916), Pekelharing-Ringer 
(1911), Ringer (1918), Rohonyi (1912), S0rensen (1909). 

Phosphatase. Adler (1915). 

Rennet. Allemann (1912), Van Dam (1908, 1909, 1912, 1915), 
Funk-Niemann (1910), Madsen-Walbum (1906), Michaelis- 
Mendelsohn (1913), Michaelis-Rothstein (1920), Milroy (1915), 
Thaysen (1915). 

Salivary diastase (ptyalin). Cole (1903), Hahn-Harpuder 
(1920) Michaelis-Pechstein (1914), Ringer-Trigt (1912). See 
amylase. 

Taka-diastase. Okada (1916). 

Trypsin. Auerbach-Pick (1913), Hahn-Mickalik (1921), Ka- 
nitz (1902), Michaelis-Davidsohn (1911), Northrop (1921, 1922), 
Palitzsch-Walbum (1912). Ringer (1921), Robertson-Schmidt 
(1908). 

Theory of action. Barendrecht (1920), Euler (1920), Falk 
(1921), Loeb (1909), Michaelis (1909. 1914), Michaelis-Davidsohn 
Mad 1911), Rohonyi (1911), Van Slyke-Cullen (1914). 

Urease. Barendrecht (1920), Lovgren (1921), Onodera (1915), 
Rona-Gyorgy (1920), Rona-Petrov (1920), Van Slyke-Cullen 
(1914), Van Slyke-Zacharias (1914). 

Equilibria. The hydrogen electrode and indicators in the 
determination of affinity constants, free energy, hydrolysis, etc. 

References. Adolf-Pauli (1921), Bjerrum (1907-21), 
Boeseken-Kerstjens (1916), Bogue (1920), Chow (1920), 
Denham (1908), Eucken (1907), Ellis (1916), Ferguson' (1916), 
Frary-Nietz (1915), Fricke (1920), Hardman-Lapworth (1911), 
Harned (1915-1922), Heyrovsky (1920), Jahn (1900, 1901), 
Kanitz (1921), Lewis (1908, 1912, 1913), Lewis-Brighton-Se- 
bastian (1917), Lewis-Randall (1914), Linhart (1919), Loffler- 
Spiro (1919), Loomis-Acree (1911), Loomis-Essex-Meacham 
(1917), Lowenherz (1896), Margaillan (1913), McBain-Coleman 
(1914), Maclnnes (1919), Merrill (1921), Nernst (1889), Newbery 



APPLICATIONS 335 

(1914), Noyes-Ellis (1917), Noyes-Freed (1920), Richards-Dun- 
ham (1922), Rosenheim-Leyser (1921), Tizard (1910), Tizard- 
Boeree (1920), Tolman-Greathouse (1912). See also Chapters 
IV, VI, XVI. 

Explosives. 

References. Farmer (1920), Angeli-Errani (1920). 

Feces. See "Digestive System." 

Filtration. Hydrogen ion concentration, through its influ- 
ence upon the dispersion of certain colloids and upon the condi- 
tioning of filter material, may control the filterability of a sub- 
stance. Holderer's thesis from Perrin's laboratory presents in 
admirable form many of the theoretical aspects of the subject. A 
republication of this rare thesis is desired. The subject is not only 
of considerable theoretical interest but also of great practical 
importance. Buffer control with indicator tests' may in many in- 
stances facilitate filtrations upon an industrial as well as a labo- 
ratory scale. 

References. Aubel-Colin (1915), Holderer (1909, 1910, 1911, 
1912), Homer (1917), Loeb (1919), Schmidt (1914), Strada (1908), 
Wilson (1921), Wilson-Copeland-Heisig (1921), Wilson-Heisig 
(1921). See also "Electrophoresis." 

Foods, pH of. The National Canners' Laboratory has made 
a number of determinations of the pH of canned foods. See 
"Canning." See also "Milk," "Cheese," "Wine," "Beer," "Vine- 
gar," references given by Clark and Lubs (1917) 1 and the paper 
by McClendon and Sharp (1919). The influence of the pH upon 
the stability of a "vitamine" has been studied by La Mer (1921), 
and Campbell, LaMer and Sherman (1922). cf. Harden and 
Zilva (1918). For sterilization of canned goods see "Disinfec- 
tion" under "Bacteriology" and "Canning". 

Glass, effect of, on reaction of solutions. 

References. Esty-Cathcart (1921), Ewe (1920), Fabian-Stull 
(1921), Levy-Cullen (1920), Russell-Nichols-Stimmel (1920). 

Glucose, decomposition of, as influenced by pH. 

References. Elias-Kolb (1913), Euler-Hedelius (1920), Hen- 
derson (1911), Mathews-McGuigan (1907), Michaelis-Rona 

1 Some of the pH values given by Clark and Lubs for acidified or alka- 
linized extracts have been misquoted as the pH values of the original 
material. 



336 THE DETERMINATION OF HYDROGEN IONS 

(1909-1912), Nef (1913), Rona-Arnheim (1913), Rona-Doblin 
(1911), Rona-Wilenko (1914). Also references in Woker. 

Hemolysis , 

References. Atkin (1911, 1914), Cook-Mix-Culvyhouse (1921), 
Coulter (1921), Fenn, (1922), Fuhner-Neubaur (1907), Gros 
(1910), Haffner (1920), Hellens (1913), Jodlbauer-Haffner (1920, 
1921), Jordan (1903), Kozawa (1914), Krogh (1909), Lagrange 
(1914), Michaelis-Skwirsky (1909), Michaelis-Takahashi (1910), 
Stevens-Koser (1920), Teague-Buxton (1907), Walbum (1914, 
1915). 

Hydrolysis. The reaction between an acid and a base is 
reversible. 

HA + BOH ?=± BA + H 2 

♦ 

There are present then both free acid and free base even when 
the two are mixed in equivalent proportions. This last condition 
can be duplicated by making up the solution in the first place 
with the pure salt. The above reaction then goes from right to 
left until the equilibrium state is reached and the process is 
called hydrolysis, because it may be regarded as a splitting 
of water molecules. 

Now the resulting acid and base ionize, the one tending to 
increase the hydrogen ion concentration, the other tending to 
increase the hydroxyl ion concentration. If the acid is more 
highly dissociated than the base the solution will contain more 
hydrogen ions than hydroxyl ions; and if the base is more highly 
dissociated than the acid the solution will contain more hydroxyl 
than hydrogen ions. Since the magnitude of a dissociation con- 
stant is a measure of dissociation tendency the reaction of a salt 
solution will depend upon the relative magnitudes of the K a 
and Kb constants of the component acid and base. 

In a solution of the salt, BA, we have present BA, B+, A - , 
HA, BOH, H+ and OH.~ 

By the rule of electrical neutrality [A~] + [OH"] = [B + ] + 
[H+]. Since total acid = total base, [HA] + [A~] + [BA] = [B+] 
-f [BOH] + [BA]. Introducing the acid and the base equilib- 
rium equations and the relation [H + ] [OH - ] = K w and combining 
these equations we have 



mn = V K - ' 



K b (K. + [Ai) 



APPLICATIONS 337 

If now Kb and K a are small in relation to [B+] and [A - ], and 
if the solution is sufficiently dilute so that [B+] and [A - ] each 
approximate the salt concentration [S], then approximately 



[h+] = V Kw i^ 



Cf. formula for isoelectric point of ampholyte. When K a = Kb, 
[H+] = 10- 7 , pH = 7. 

If we are dealing with a salt, the acid component of which 
is very "strong" we may regard the acid set free by the hydroly- 
sis of the salt as completely dissociated. [HA] in the above equa- 
tions is placed equal to zero and we then derive 

[H+]= ^(Kh + [B+]) 
" Kb 

If now Kb is small in relation to [B+] and if [B + ] approxi- 
mates [S] 

[H+] approximates \— - [S] 
™ Kb 

Conversely when the base is very strong and when the same 
assumptions made above are maintained 



[H + ] approximates W 



K a K v 



[S] 



References. See treatment by Bjerrum (1914), example by 
Denham (1908), and numerous references under "Equilibria." 

Indicator Constants. See Prideaux and Chapters IV and 
VIII. 

, References. Clark-Lubs (1917), Gillespie (1920), Paulus-Hut- 
chinson-Jones (1915), Kolthoff (1918-1922), Michaelis (1920), 
Michaelis-Gyemant (1920), Michaelis-Kriiger (1921), Rosenstein 
(1912), Schaeffer-Paulus-Jones (1915), Salm (1904), Tizard (1910). 

Indicators, natural. 

References. Bribaker (1914), Crozier (1916, 1918), Haas (1916), 
Pozzi-Escot (1913), Sacher (1910), Scheitz (1910), Stephanides 
(1916), Trillat (1916), Walbum (1913), Watson (1913). See also 
Perkin and Everest. 



338 THE DETERMINATION OF HYDROGEN IONS 

Industrial Processes. See every subject in this chapter. 
Also the following special references. 

References. Brewster-Raines (1921), Clark-Zoller-Dahlberg- 
Weimar (1920), Keeler (1922), Lubs (1920), Searle (1920), Wil- 
son-Copeland-Heisig (1921), Wilson-Heisig (1921), Zoller/1921), 
and references on "Water Works" and "Leather." 

Isoelectric Points. See Chapter I. 

References. Brossa (1915), Cohn (1920-1922), Cohn-Gross- 
Johnson (1920), Eckweiler-Noyes-Falk (1920), Fodor (1920), 
Loeb (1918-1922), Michaelis (1911-1920), Michaelis-Bien (1914), 
Michaelis-Davidsohn (1910-1913), Michaelis-Grineff (1912), 
Michaelis-Mostynski (1910), Michaelis-Pechstein (1912), Michae- 
lis-Rona (1919), Michaelis-Takahashi (1910), Mills (1921), 
Rona-Michaelis (1910), S0rensen (1912, 1917), Stuber-Funck 
(1921), Szent Gyorgyi (1921), Thomas-Kelley (1922). 

Leather and Tanning. 

References. Atkin (1922), Atkin-Atkin (1920), Atkin-Thomp- 
son (1920), Balderston (1913), Procter (1921), Procter-Wilson 
(1916), Povarnin (1915), Sand-Law (1911), Thomas-Baldwin 
(1919), Thomas-Foster (1921), Thomas-Kelly (1921, 1922), 
Wilson (1917, 1921), Wilson-Daub (1921), Wilson-Kern (1921), 
Wood-Sand-Law (1911). See also "Proteins." 

Milk. 

References. Allemann (1912), Aron (1914), Baker-Breed (1920)/ 
Baker-Van Slyke (1919), Chapman (1908), Clark (1915), Clark- 
Cohen (1922), Cooledge-Wyant (1920), van Dam (1908, 1918), 
Davidsohn (1912, 1913), Foa (1905, 1906), Hastings-Davenport 
(1920), Jones (1921), Kramer-Green (1921), Laqueur-Sackur 
(1903), Milroy (1915), Palmer-Dahle (1922) Rogers-Deysher- 
Evans (1921), Rona-Michaelis (1909), Schultz-Chandler (1921), 
Schultz-Marx-Beaver (1921), Sommer-Hart (1919, 1920), Stut- 
terheinn, Szili (1917), Taylor (1913), Terry (1919), Till- 
mans-Obermeier (1920), Van Slyke-Baker (1918, 1919). See also 
"Cheese" and "Protein." 

Neuro-physiology. 

References. Adrian (1920), Bottazzi-Craifaleanu (1916), Chid 
(19,07), Garry (1920), Grant (1920), Mansfield-Szent Gyorgyi 
(1920), Mayer (1916), Moore (1919), Neugarten (1919), Zotter- 
man (1921). See also "Blood," (the respiration phase) and 
"Comparative and General Physiology." 



APPLICATIONS 339 

Permeability of cells. 

References. Bethe (1922), Clowes-Smith (1922), Collander 
(1920), Donnan (1911), Haas (1916), Harvey (1911, 1913), Haynes 
(1921), Holderer (1911), Jacob j (1920), Lillie (1909), Moore-Roaf- 
Webster (1912), Oden (1916), Reemelin-Isaacs (1916), Snapper 
(1913), Stiles-Jorgensen (1915), compare Filtration. 

Phagocytosis. 

References. A. Evans (1921, 1922), Hamberger-Heckma (1908) , 
Koltzoff (1914), Radsma (1920), Sawtchenko-Aristovsky (1912), 
Schwyzer (1914). 

Pharmacology, etc. pH in relation to properties, activity, 
deterioration, and assay or detection of drugs. 

References. Adams (1917), Crane (1921), Evers(1921),v.Groer- 
Matula (1920), Hanzlik (1920, 1921), Kolthoff, (1920, 1922), 
Leech (1922), Levy-Cullen (1920), Macht-Shohl (1920), Meier- 
Kronig (1921), Mellon-Slagle-Acree (1922), Menten (1920), 
Moore (1920), Rippel (1920), Rona-Bach (1920), Shohl-Deming 
(1921), Snyder-Campbell (1920), Sollmann (1917), Tsakalotos- 
Horsch (i914), Williams-Swett (1922), Zoccola (1918). 

Phyto-pathology and Physiology. 

References. Atkins (1922), Chambers (1921), Clevenger (1919), 
Crozier (1919), Harvey (1920), Hixon (1920), Lapicque (1921), 
MacDougal (1921), Martin (1921), Schmitz (1919), Schmitz- 
Zeller (1919), Webb (1919), Wherry (1918-22), Wolf-Foster 
(1921), Wolf-Shunk (1921), Zeller-Schmitz (1919). 

See "Plant Distribution," "Comparative and General Physi- 
ology," "Soil." 

Plant Distribution. Wherry, working with a simple field 
kit, has carried indicators into the field and has correlated the 
habitats of several plant species with the pH of their soils. 

Investigations by O. Arrhenius in Sweden, by Olsen in Denmark 
and by Atkins in England and India have confirmed Wherry's 
observation that the pH of the soil is of great significance. 

Such information has contributed toward methods of cultivat- 
ing the blueberry and wild-flowers hitherto unknown or un- 
common in garden and greenhouse. 

References. Arrhenius (1920, 1922), Atkins (1921, 1922), 
bomber (1921), Emerson (1921), Fisher (1921), Gail (1919), 
)lsen (1921), Wherry (1920-1922). See also "Phytopathology 
tnd Physiology," " Soils," "Water," and especially " Bacteriology." 



34:0 THE DETERMINATION OF HYDROGEN IONS 

Proteins, by reason of their chemical structure, are amphoteric. 
As such they are subject to the pH of aqueous dispersing media 
as are the simple ampholytes. Though complete equilibrium 
equations are difficult to formulate we should expect the occur- 
rence of pH points and zones comparable to the isoelectric points 
and zones of simple ampholytes. Experimentally these have 
been found. These are also points of optima, or minima, for 
various properties of protein solutions (e.g. minimal electrophore- 
sis, viscosity and osmosis). If the solubility of the protein itself 
is less than that of its acid or basic salts, the protein can be pre- 
cipitated at or near the isoelectric point (e.g. analysis and com- 
mercial preparation of casein). Closely related is the adjustment 
of pH favoring separation of crystals. Proteins are unable to 
penetrate many membranes but are able to enter into an acid- 
base equilibrium and thus exhibit many interesting relations in 
Donnan equilibria (S0rensen, Loeb). 

The outstanding difficulty in treating proteins as electrolytes 
is the establishment of exact quantities for concentrations or 
activities which must necessarily be used in formulating equilib- 
rium equations. The mathematical treatment by Michaelis 
and by S0rensen, and especially the painstaking experimental 
investigations to which S0rensen and his coworkers have devoted 
several years have advanced the subject beyond dependence on 
mere analogy to the conduct of simple ampholytes. 

References. Adolf -Spiegel (1920), Agostino-Quagliariello (1912), 
Atkin (1920), Bogue (1921), Bovie (1920), Bugarszky-Liebermann 
(1898), Burrows-Cohn (1918), Chiari (1911), Chick (1913), 
Chick-Martin (1910-13), Clark-Zoller-Dahlberg-Weimar (1920), 
Cohn (1920-22), Cohn-Gross-Johnson (1920),Davis-Oakes-Browne 
(1921), Ferguson-France (1921), Field (1921), Fodor (1920-21), 
Haas (1918), Handovsky (1910), Hardy (1899, 1905), Henderson- 
Cohn-Cathcart-Wachman-Fenn (1919), Henderson-Palmer-Neu- 
burgh (1914), Hill (1921), Hitchcock (1922), Laqueur-Sackur, 
(1903), Lloyd (1920, 1922), Loeb (1918-22), Manabe-Matula 
(1913), Michaelis (1909), Michaelis-Airila (1921), Michaelis- 
Mostynski (1910), Michaelis-Rona (1910, 1919), Michaelis- 
Szent Gyorgyi (1920), Mills (1921), Okuda-Zoller (1921), Oryng- 
Pauli (1915), Palmer-Atchley-Loeb (1921, 1922), Patten-John- 
son (1919), Patten-Kelems (1920), Pauli (1903-1922), Pauli- 



APPLICATIONS 341 

Handovsky (1908-10), Pauli-Matula (1919), Pauli-Samec (1909- 
14), Pauli-Wagner (1910), Pechstein (1913), Procter-Wilson 
(1916), Quagliariello (1912), Resch (1917), Robertson (1907- 
1918), Rohonyi (1912), Ryd (1917, 1918), Sharp-Gortner (1922), 
Schmidt (1916), Schorr (1911), Sollmann (1917), S0rensen (1917- 
1921), S0rensen & coworkers (1917), S0rensen-Jiirgensen (1911), 
Spiro (1904, 1913), Starke (1900), Szent-Gyorgyi (1920, 1921), 
Thomas (1921), Wagner (1921), Wintgen-Kriiger (1921), Wint- 
gen-Vogel (1922), Ylppo (1913), Zoller (1921). See also "Iso- 
electric Point." 

Salt-Action, theory and effects in relation to pH. See Chap- 
ters I, II, and VII. 

References. Abegg-Bose (1899), Arrhenius (1888, 1889), Aker- 
lof (1921), Brightman-Meachem-Acree (1920), Chick-Martin 
(1912, 1913), Falk (1918, 1920), Gillespie- Wise (1918), Harned 
(1915), Haynes (1921), Hofmeister (1891), Holm-Sherman (1921- 
1922), Kolthoff (1916-22), Lloyd (1916), Loeb (1906-1922), 
McBain-Coleman (1914), McClendon-Mitchell (1912), Michaelis 
(1914, 1920), Michaelis-Rona (1909), Michaelis-Szent Gyorgyi 
(1920), Michaelis-Timenez Dias (1921), Northrop (1920), Poma 
(1914), Poma-Patson (1914), Prideaux (1919), Rose-Kraybill-Rose 
(1920), Rosenstein (1912), Ryd (1917), Shearer (1920), Sherman- 
Thomas (1915), S0rensen-Palitzsch (1913), S0rensen-S0rensen- 
Linderstr0m Lang (1921), Spiro (1921), Szent-Gyorgyi (1920), 
Szyszkowski (1907), Thomas Baldwin (1919), Wells (1920), See 
especially references in Chapter II on "Activity." 

Serology. See also Acid Agglutination of Bacteria, Hemolysis, 
Bacteriology, Proteins, Colloids. 

References. Amako (1911), Atzler (1914), Brooks (1920), 
Buchanan (1919), Coulter (1921), Enlows (1922), Evans (1921, 
22), Field-Teague (1907), Hirsch-Peters (1922), Homer (1917, 
1918, 1919), Landensteiner (1913), Landensteiner-Prasek (1913), 
Langenstrass (1919), Lindenschatt (1913), Leschly (1916), Ma- 
son (1922), Michaelis-Davidsohn (1912), Neukirch (1920), No- 
guchi (1907), Ruppel (1920), Tulloch (1914, 1918). 

Sewage. 

References. Clark-Cohen (1922), Wilson-Copeland-Heisig 
(1921), Wilson-Heisig (1921). 






342 the determination of hydrogen ions 

Soap Solutions. 

References. Beedle-Bolam (1921), McBain (1920), McBain- 
Bolam (1918), McBain-Martin (1918), McBain-Salmon (1920). 

Soil Acidity has been confused by the complexities of titri- 
metric procedures, has been neglected, or has been considered to be 
an unreality by one or another school. Gillespie (1916) obtained 
good agreement between pH values of soil extracts determined 
by means of the hydrogen electrode and again by means of indi- 
cators. The practical significance of this is now revealed by 
studies which show characteristic pH values for well-defined types 
of soil, which show correlations between the pH of soil extracts 
and the growth of beneficial or harmful microorganisms, and 
which show correlations between the natural distribution of 
plants and the pH of the soils in which they are found. 

References. Arrhenius (1921, 1922), Atkins (1922), Bjerrum- 
Gjaldbaek (1919), Blair-Prince (1920), Carr (1921), Comber 
(1920), Conner (1921), Crouther (1920), Demolon (1920), Dug- 
gar (1920), Erdman (1921), Fisher (1914, 1921), Gainey (1918, 
1922), Gillespie (1916-1918), Gillespie-Hurst (1918), Hibbard 
(1921), Hoagland (1917-1918), Hoagland-Christie (1918), Hoag- 
land-Sharp (1918), Hudig-Strum (1919), Joffe (1920), Jones- 
Shive (1920), Kappen (1916), Kappen-Zapfe (1917), Kelley- 
Cummins (1921),. Knight (1920), Kobayashi (1920), Lipman- 
Joffe (1920), Lipman-Waksman-Joffe (1921), Loew (1903), 
xMcCall-Haag (1920, 1921), MacDougal (1920), Martin (1920, 
1921), Meier-Halstead (1921), Morse (1918, 1920), Oden (1916- 
21), Olsen (1921), Plummer (1918), Rice-Osugi (1918), Robinson 
(1921), Robinson-Bullis (1921), Saidel (1913), Salter-Mcllvaine 
(1920), Schollenberger (1921), Sharp-Hoagland (1916, 1919), 
Stephenson (1919, 1921), Stocklasa (1922) Swanson-Latshaw- 
Tague (1921), Tijmstra (1917), Truog (1918), Truog-Meacham 
(1919), Waksman (1922), Weis (1919), Wherry (1916-1922). 
See also "Plant Distribution." 

Solubility. The true solubility of a compound may be 
regarded as independent of the hydrogen ion concentration of a 
solution; but if the compound is an acid, base, ampholyte or salt 
some of the material present in solution is ionized and this portion 
is governed by the ionic equilibrium of which the hydrogen ion 
concentration is a part. Therefore the total solubility which is 



APPLICATIONS 343 

generally of more importance than the true, partial solubility 
is a function of pH. 

[H+] [A-] 
Consider the equilibrium — =77: — = K a and assume that 

LH-AJ 

the solubility of the acid HA itself is low so that we shall not 
encounter the difficulties inherent in the treatment of concen- 
trated solutions. If the acid is present in the solid phase [HA] 
is maintained constant and is the partial solubility, S p . On 
combining the constants in the above equation we have [H + ] 
[A - ] = K s where K s is the solubility product. The total solu- 
bility, S t is then equal to the true partial solubility, S p , plus [A - ] or 

*•_« , j^ q _* n H+] ± Ka l 

»t — &p -r rjj+i' or °t — & p ru+i 

If there is present no salt of the acid to furnish [A - ] 

[Hi 2 = K 8 
or 

pH = - } log K 8 

For the case of calcium carbonate, the [C0 3 ] from which is 
controlled by [H + ], see "Carbonate Equilibria." 

References. See any text on physical chemistry and "Carbon- 
ate Equilibria," "Protein," "Equilibria," etc. 

Staining. 

References. Agulhon-Leobardy (1921), Bethe (1922), Jodl- 
bauer-Haffner (1921), MacArthur (1921), Michaelis (1920), 
Ponselle (1919), Rohde (1920). 

Surface Tension. 

References. Adam (1921), Bottazzi-Agostino, Ellis (1911), 
Haber-Klemensiewicz (1909), Hartridge-Peters (1920), Micha- 
elis (1909), Schwyzer (1914), Traube (1920), Williams (1920), 
Willows-Hatschek (1919), Windish-Dietrich (1919-1922). 

Sweat. 

References. Clark-Lubs, (1917), Talbert (1919). • 

Tautomerism other than of indicators. 

References. Biddle-Watson (1917), Fraenkel (1907) Mur- 
chauser (1920), Nelson-Beegle (1919). 

Tissue Culture. 

References. Felton (1921), Fischer (1921), Lewis-Felton (1921). 



344 THE DETERMINATION OF HYDROGEN IONS 

Urine and Kidney Functions. The excretion of acids and 
bases in the urine is one of the mechanisms by which the hydrogen 
ion concentration of the blood is preserved constant. For this 
reason the determination of the acid-base equilibria in the urine 
in their relation to the potential acid-base intake in the food and 
the degree of oxidation of food material is of importance in 
fundamental physiological researches and in clinical studies. 
Besides references to be found under "Blood" the following are 
some of the more special references on urine. 2 

References. Auerbach-Friedenthal (1903), Biehler (1920), Biltz- 
Hermann (1921), Blatherwick (1914), Bugarszky (1897), Carr 
(1921), Collip-Backus (1920), Cushny (book 1917), Fiske 
(1920, 1921), Fitz-Van Slyke (1917), Foa (1905), Gamble (1922), 
Guillaumin (1920), Hanzlik (1920), Haskins (1919), Hasselbalch 
(1916), Henderson (1910, 1911, 1914), Henderson-Palmer (1913) 
Henderson-Spiro (1908), Hober (1902), Hober-Jankowsky (1903) 
Hollo (1921) a Howe-Hawk (1914), Macleod-Knapp (1918) 
Marshall (1922), Nagayama (1920), Nelson-Williams (1916) 
Newburgh-Palmer-Henderson (1913), Palmer-Henderson (1915) 
Palmer-Salvesen-Jackson (1920), Quagliariello-d'Agostino (1912) 
Reemelin-Issacs (1916), Rhorer (1901), Ringer (1909, 1910) 
Rohde (1920), Schemensky (1920), Schloss-Harrington (1919) 
Shohl (1920), Skramlik (1911), Stillman-Van Slyke (1917), Tal- 
bert (1920), Van Slyke-Palmer (1919, 1920). 

Vinegar. 

Reference. Clark-Lubs (1917), Brode-Lange (1909), Kling- 
Lassieur-Lassieur (1922). 

Water (sea and fresh). The carbonate equilibrium maintains 
sea water at a very constant pH which has doubtless varied with 
the C0 2 tension of the atmosphere in geological ages and which 
varies somewhat with the temperature, and locally with accretions 
from rivers and springs and contact with geologic deposits. The 
wider aspects of the carbonate equilibria involved have been 
described in Henderson's Fitness of the Environment. The chart- 
ing of the pH values for different regions of the seas has been 
of aid in oceanographic surveys and in some instances has been 
of value in the study of plant and animal distribution. (See 
"Plant Distribution" and "Comparative Physiology.") 

* See Clark and Lubs (1917) for some examples 'of the application of the 
sulfon phthalein indicators to the determination of the pH of urines. 



APPLICATION'S 345 

Fresh waters are influenced chiefly by the deposits with which 
they come in contact. pH determinations in the field are of aid to 
the geologist in demarking waters of limestone origin (Wherry 
private communication) . 

In the clarification of water by "alum" or "iron" coagulation 
the pH of the final mix determines the percentage coagulant thrown 
out, the time required for floe formation and the efficiency of 
color- and turbidity-removal. There is also a probable relation 
to the efficiency of the filtration process itself. 

The hydrogen ion enters into every equilibrium of importance 
to water softening and to corrosion. 

References. Auerbach (1904), Baylis (1922), Buswell (1922), 
Corti-Alvarez (1918), Crozier (1920), Gaarder (1916-1917), 
Greenfield-Baker (1920), Haas (1916), Henderson (1913), Hen- 
derson-Cohn (1916), Heyman (1920), Kolthoff (1921), Loeb 
(1904), McClendon (1916, 1917), Mayer (1919), Massink (1920), 
Massink-Heyman (1921), Michaelis (1914, 1921), Palitzsch 
(1911, 1915, 1916), Powers (1921, 1922), Prideaux (1919), Ringer 
(1908), Ruppin (1909), Saunders (1921), Shelf ord (1919), Smith 
(1919), Snook (1915), S0rensen-Palitzsch (1910-13), Stephanides 
(1916), Tillmans (1919, 1921), Trillat (1916), Wagner-Enslow 
(1922), Walker-Kay (1912), Wells (1921), Wolman-Hannan (1921). 

Water, pure. Ionization of. 

References. Kohlrausch-Heydweiller (1894), Lewis, Brighton 
and Sebastian (1917), Nernst (1894), Ostwald (1893), Wijs (1893). 

Wine Acidity. Besides influencing the fermentations, the pH 
of wine has been found to correlate in a general way with the acid 
taste. 

References. Casale (1919), Dutoit-Dubroux (1910), Paul 
(1914, 1915, 1916), Quartaroli (1912). 






BIBLIOGRAPHY 

Knowledge is of two kinds . We know a subject ourselves, or we 
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Abbreviations follow for the most part the system adopted by Chemical 
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Fermentforschung, 4, 191. 
Abegg, R. 1902 Uber die Komplexbildung von Quecksilbersalzen. Z. 

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Abegg, R., Atterbach, F., and Luther, R. 1909 Zur Frage des Null- 

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15, 63. 
Abegg, R., Auerbach, F., and Luther, R. 1911 Messungen elektromo- 

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Bunsen-Gesellschaft, No. 5. Halle, 1911. 
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Abel, E. 1920 Kinetik der Wasserstoffsuperoxyd-Jod-Reaktion. Z. 

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346 



BIBLIOGRAPHY 347 

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Adam, A. 1921 Ueber das H-Ionenoptimum der Kopfchenbakterien des 
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Adam, A. 1921 Ueber den Einfluss der H-lonenkonzentration des Nahr- 
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Adam, A. 1922 Ueber die Bedeutung der Eigenwasserstoffzahl (des 
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Adams, E. Q., and Rosenstein, L. 1914 The color and ionization of 
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Adam, N. K. 1921 The properties and molecular structure of thin films of 
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Adams, H. S. 1917 The thermal decomposition of the oxytocic principle 
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Adler, L. 1915 tJber die Phosphatasen im Malz. Biochem. Z., 70, 1. 

Adler, L. 1915-16 Uber den Einfluss der Wasserstofflonen auf die Wirk- 
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Adler, H. M., and Blake, G. 1911 The retention of alkali by the kidney 
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Adolf, M., and Pauli, W. 1921 Die physikalisch-chemische Analyse 
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Adolf, M., and Spiegel, E. 1920 Untersuchungen liber physikalische 
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Biochem, Z., 104, 175. 

Adrian, E. D. 1920 The recovery process of excitable tissues. Part I. 
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348 THE DETERMINATION OF HYDROGEN IONS 

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350 THE DETERMINATION OF HYDROGEN IONS 

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V 



352 THE DETERMINATION OP HYDROGEN IONS 

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354 THE DETERMINATION OF HYDROGEN IONS 

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356 THE DETERMINATION OF HYDROGEN IONS 

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358 THE DETERMINATION OF HYDROGEN IONS 

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360 THE DETERMINATION OF HYDROGEN IONS 

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362 THE DETERMINATION OF HYDROGEN IONS 

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364 THE DETERMINATION OF HYDROGEN IONS 

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366 THE DETERMINATION OF HYDROGEN IONS 

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370 THE DETERMINATION OF HYDROGEN IONS 

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372 THE DETERMINATION OF HYDROGEN IONS 

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374 THE DETERMINATION OF HYDROGEN IONS 

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\f 



376 THE DETERMINATION OF HYDROGEN IONS 

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378 THE DETEKMINATION OF HYDROGEN IONS 

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380 THE DETERMINATION OF HYDROGEN IONS 

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382 THE DETERMINATION OF HYDROGEN IONS 

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384 THE DETERMINATION OF HYDROGEN IONS 

Harned, H. S. 1916 The hydrogen and chlorine ion activities of solu- 
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Harvey, E. N. 1920 The action of acid and of light in the reduction of 
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BIBLIOGRAPHY 385 

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386 THE DETERMINATION OF HYDROGEN IONS 

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BIBLIOGRAPHY 387 

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388 THE DETERMINATION OF HYDROGEN IONS 

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390 THE DETERMINATION OF HYDROGEN IONS 

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392 THE DETERMINATION OF HYDROGEN IONS 

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394 THE DETERMINATION OP HYDROGEN IONS 

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396 THE DETERMINATION OF HYDROGEN IONS 

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398 THE DETERMINATION OF HYDROGEN IONS 

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400 THE DETERMINATION OP HYDROGEN IONS 

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402 THE DETERMINATION OF HYDROGEN IONS 

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BIBLIOGRAPHY 



403 



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404 



THE DETERMINATION OF HYDROGEN IONS 



V 



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BIBLIOGRAPHY 405 

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406 THE DETERMINATION OF HYDROGEN IONS 

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408 THE DETERMINATION OF HYDROGEN IONS 

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410 THE DETERMINATION OF HYDROGEN IONS 

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412 THE DETERMINATION OF HYDROGEN IONS 

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414 THE DETERMINATION OF HYDROGEN IONS 

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416 THE DETERMINATION OF HYDROGEN IONS 

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418 THE DETERMINATION OF HYDROGEN IONS 

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420 THE DETERMINATION OF HYDROGEN IONS 

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422 THE DETERMINATION OF HYDROGEN IONS 

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424 THE DETERMINATION OF HYDROGEN IONS 

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426 THE DETERMINATION OF HYDROGEN IONS 

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428 THE DETEKMINATION OF HYDROGEN IONS 

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430 THE DETEBMINATION OF HYDROGEN IONS 

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432 THE DETERMINATION OF HYDROGEN IONS 

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434 THE DETERMINATION OF HYDROGEN IONS 

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436 THE DETERMINATION OF HYDROGEN IONS 

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438 THE DETERMINATION OF HYDROGEN IONS 

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BIBLIOGRAPHY 439 

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440 THE DETERMINATION OF HYDROGEN IONS 

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442 THE DETERMINATION OF HYDROGEN IONS 

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444 THE DETERMINATION OF HYDROGEN IONS 

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446 THE DETERMINATION OF HYDROGEN IONS 

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448 THE DETERMINATION OF HYDROGEN IONS 

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